I joined a campaign around the start of paragon tier and now at level 17 the DM is unfortunately moving away. I'm the only one who's DMed before so I was chosen to take over after he's gone. The biggest problem is that he has introduced a fair number of outrageously powerful homebrew items. As an example last encounter we got a staff that gave +20 attack and +7 damage and ignored all resistances. The distribution of these items also hasn't been equal, the ranger has gotten nothing but enchanted arrows while the bard quite literally has more than 2000 health at level 17. Our attack values range from +20 to +70 and the defenses have a similar ranges. The previous DM basically made every encounter feature gods that have attack and defense in the 100+ range then openly talked about he had to nerf them down to our level. I have no idea how to make encounters work with these numbers but don't want to make the characters that rely heavily on these mechanics have to completely rebuild their character's item set. Is there any good way to handle this?
Talk to your players as people
"Hey guys, so I'm taking over to finish out this campaign. You know and I know that this game is already complicated enough, and the previous DM did a lot of game design with math the books don't support at all, and I'm not going to be able to match or meet that. So here's what we're gonna do - I'm going to downstat the items to powerful but within tolerances for what the books support. This also means if you're fighting gods or whatever they, too, will not have +100 Attack Bonuses or 10,000 hitpoints or so on. It'll be proportional, and I'll try to get you some fun encounters and a good story. That's what I can do."
If the players aren't happy with that, then everyone can save each other's time - you can't run on the previous GM's weird math, even if you tried, and they won't have a good time watching you flail in the dark on how to do so. If the players are only there because "More hitpoints = more awesome" I don't really think there was much of a game to begin with.
Tell them what you're facing and if they're ok with it, you can have a great game continuing onward, it's just going to work better when you've got math the books support, the forums and all the other players out there with expertise, can give you advice on.
"Nerfing" down-stat-ing, etc.
You can basically pull weapons from the DMG and use those stats. Given how over the top the game has been, I would consider maybe giving items an extra feature or allow it to do something really powerful but a limited amount of times.
"Ok, so the staff is using the highest magical weapon stats you'd normally get, and I'm giving it a daily power to ignore resistances for 3 combat rounds. Not all the time, but you can figure out when you want to use it and it's still really powerful!"
If some of the characters are vastly underpowered compared to others after you've done the downstats, which, by the way, you can now compare using the core rules now that everything isn't in super-high math mode, you can look at what kinds of weapons/armor/etc. will even out the party.
They've been fighting Gods, I'm pretty sure they can find, have gifted, or something other magic items to round that out.
There's a lot of people who have written about "reskinning" monsters in 4E. "Reskin" basically means you change the description of the monster, but keep the same math. The example I remember was someone having demons that were simply using the math and stats for goblins. "I'm fighting hordes of demons!" etc.
You're going to do the same thing here for the gods or whatever the players face next.
If you want to change anything to keep the epic feel, I'd consider downgrading the hardness/hitpoints for inanimate objects and scenery. Instead of epic gods doing 300 points of damage, they can do the appropriate 17th level damage but things like castle walls, giant boulders, etc. might have 1/2 or 1/4th their normal hitpoints - meaning the monsters and the uber weapons the characters are wielding all blow through these things and keep that feeling of mythical damage and power without having to make you design new math for the game.
What makes fights fun in 4E is great environments and staged monster fights with fun gimmicks, not bigger numbers. So focus on those things and that's where you'll find more fun to be had.
So, a lot of people mentioned this in comments but it doesn't appear to be adequately covered in the answers yet:
Start a new campaign!
You will save yourself immense amounts of headache. You should, of course, have a conversation with your former party members who are now your players about this, but you almost certainly can't take over the other GMs campaign. This isn't just because his campaign has weird items, it because his campaign isn't yours. Having taken over campaigns myself, and having trained others to do so for me, I can tell you that getting this to work well is never a sure thing and practically requires that the GM stepping down sit down with the new GM and talk them through stuff. If the leaving GM is taking an active role in your preparations, then you may be able to actually take over the campaign with just a few modifications (you should still talk this over with your players, though). If not, you are going to have several other problems as soon as you try to actually run the campaign, many of which (unless you've done this before) you won't expect beforehand:
Iconic NPCs won't work right and/or will upset some players
The way the previous GM ran important NPCs is going to be different than how you run them. The common personality types, dialogue patterns, etc are all going to change. This isn't really a problem, except in the case of NPCs the party frequently interacts with that are far from the kinds of characters you normally run. These NPCs will seem very 'out of character' or 'forced' when you run them, leading the players of characters with strong ties to said NPC to become upset and/or you (as a former player) to become upset yourself.
The things your new players liked best about the game will probably not be as good as it was before
Unless you are unilaterally superior as a GM to your predecessor (which is possible), the thing your previous GM was best at they were probably better at than you. You are going to struggle with meeting the players' inflated expectations in the former GM's specialty.
This is likely a non-issue given the nature of the previous game but if the previous game did contain some kind of overarching plot (or, worse, several incomplete plotlines of differing lengths) you will have trouble tying up all the loose ends. Generally this isn't a problem until someone notices one, and even then you can just admit that some things got fuzzy when you took over, but is a frequent issue nonetheless, and requires a lot of GM work.
You won't have fun
For a lot of GMs, the thing that makes GMing fun is getting to come up with all the cool stuff that the other people play in. If that's the case, you, personally, might not be able to take over another GMs campaign at all. A significant minority of the GMs I've had involved in these sorts of things run the campaign they take over just fine for a bit, but hated doing it because they were stuck running things "in someone else's world".
All of the above concerns can be mitigated (and might not even apply to you), but you should really consider whether or not they are worth mitigating. Why not start a new campaign? It will probably be a lot easier and, unless the game is crying out for closure, you will almost certainly be better served making a new one than continuing the old one.
You've definitely landed yourself in a pretty crappy situation there. The only definite way you're going to keep everyone happy is to continue DMing like the last guy did, which you're clearly not okay with. There are two solutions that I see to your problem.
Make them want to give up the items
Just outright taking the items and telling your players "Hey, these were incredibly broken and don't work in a normal game, we're not using them anymore" is a really good way to get your players angry with you. Instead, give your players a good reason to want to get rid of the items using in-game justifications.
For example, maybe you could invent a ritual that will consume these items, but give the person who sacrifices their item a really cool utility power. Maybe introduce new items that are also really awesome, but don't mess with numbers quite so much. It's way easier to have a mostly-sane game of 4e where the fighter can slide 10 once per encounter, rather than one where he has a +20 sword.
This works even better if you can get player buy-in, and maybe let the players help design these new items. You may also want to offer full or partial re-specs to allow players to make their characters work better with these new items.
Alternately, let players trade their items for roleplaying rewards. Maybe that awesome staff is something that a great archmage wants, and he offers the party ten free teleports to wherever they want in exchange. Maybe the bard can sacrifice some of his health items in exchange for a dukedom in his favorite country.
End this game quickly ,and start a new one.
If you don't think your players will go along with getting rid of their items, your only real alternative is to play a different campaign. However, it's likely that your players are invested in their current characters, and it sucks when a character you like doesn't get a good end to their story. Spend the next several sessions wrapping up as many plotlines as you can, and do your best to give the game a satisfactory conclusion. You may have to do a lot of handwaving on the combat stats of monsters during this time, since it's clear that your previous DM was doing the same. Once you feel you can end the campaign in a way that your players will be mostly satisfied with, finish it. I find that it helps to give each character their own denouement, where you let the player describe what their character would do after the campaign, and embellish a bit on the character getting their wish. I tend to ask "What does your character do after the campaign ends?", and then describe more fully what the player tells me.
This way, your players will feel more fulfilled with the end of the campaign, and less likely to revolt when you take away their shinies. You can even start the next campaign in the same world, to make your players more invested in their new characters. Since you'll have a whole new campaign, you'll be able to keep the magic items sane to start with.
No, there isn't.
Option 1: Power Everybody Up
You can give everybody gear to bring them up to parity with the most overpowered character: everybody has a god-like attack bonuses, defenses, damage, and health (with variances for stats and classes, of course).
Option 2: Nerf Everybody
Take away all of the shinies, and replace them with level-appropriate gear (or, at least, to parity with the least-powerful character's kit).
Option 3: New Campaign
Start a new campaign.
Pros and Cons
Option 1 lets the players keep their numbers high, and lets you add a static +X to all NPC attacks and defenses, with a *Y multiplier for HP. What's the difference between player ACs ranging between 5 and 15 vs. 55 and 65? A +50 bonus on NPC attacks.
Option 1 unfairly gives really awesome stuff to the characters that have contributed the least to the party getting to where it is ("what do you mean, the Ranger gets a +40 bow; he never hits anything, anyway, and I need another +5 for these gods"). It also "just" makes all of the numbers higher for the sake of being higher.
Option 2 brings the party power level back in line with what the system expects, allowing you to bring in external modules, standard monsters, etc., all without having to figure out what the "Horrifically Overpowered PC" bonus needs to be in order to maintain balance. It also dings everybody.
Option 2 nerfs everybody: even the ranger, with his measly +20, is going to drop down to a +18 (and, the loss of those awesome arrows is likely to hurt, too). Plus, "why should I have to give up my +50 Sword of Smiting just because you can't figure out how to run a campaign with it?".
Option 3 lets the current god-like characters retire into glory (potentially becoming gods in their own rights), and lets the players imagine how those characters will continue to effect the cosmos.
Option 3 forces the players to give up the characters in which they've invested so much time and creative energy, just as the story is reaching the "next level" (the level 20-30 tier).
Of all of the options, the least bad is likely to be 3: run a session or two which get the characters clearly set on the path to glory, then wrap up the campaign with some great narration about how they become gods or something. Then, start a whole new story (possibly set a hundred years later, letting the players deal with the fall-out of their past characters' actions) and keep the power level reasonable.
... well, that or start the next session with "rocks fall, everybody dies" and move on to a new system for a while ...