I realized, as I was going online to relearn probability to the point where I could be useful to you, that I wasn't sure if your DM does things the 3.5 way and only lets you crit if you roll a 19 or 20 naturally.
If so, then your crit rate (success AND failure) remains unchanged, no matter the stats, and all you get is bonus to-hit.
Average roll on a d8 is 4.5, so if you want to know your average damage per hit, there you go. Crits do an average of 9 damage. This guide assumes that, like Advantage and Disadvantage, you get no inherent bonuses to damage for having it, only what you get for landing a crit.
+2 = 10% chance of crit, 5% chance of flop.
-2 = 10% chance of crit, 5% chance of flop.
However, the thing about Advantage and Disadvantage is that, by increasing the number of times you roll, you get more chances to hit it big or fail horrendously, so that would suggest that these bonuses should factor into success or failure.
If the system he's using doesn't factor this in, point this out to your DM and see what he says about it. Go with what he says regardless of his answer as long as he understands the statement, but just make sure he knows.
If the bonuses are factored into the roll (read "treated as the natural roll") as opposed to being tacked on at the end, then it will look very different...
+2 = 20% chance of crit (crits on 17, 18, 19, 20), ?% chance of flop (1+2=3, so either advantage means you can't bungle something in this system, or it's calculated normally, the bonus added after you see the result. BRING THIS UP WITH YOUR DM).
-2: 0% chance of crit (20-2 = 18 aka not a crit. Wow, that's rough), 15% chance of flop (3-2=1 (>_<))
In this version, where the bonuses are trying to mimic the tendencies shown in the normal version, saying the buffs and debuffs are too strong is an understatement. Worse yet, it's incredibly restricting and unrealistic, as having advantage means you can't fumble, and having disadvantage means you can't crit, which makes anything that grants these bonuses to you and these debuffs to the enemy are OP AF, which makes halflings, the Lucky feat, and rogues in general OP.
And I don't even want to CONSIDER half-orc ferocity + greataxe + barbarian rage + advantage... Q-Q
However, without the use of the new "natural" number, the bonuses don't pack enough of a punch to really matter, which shoots the whole concept of Advantage and Disadvantage in the foot. The whole point of 5e was to get away from tiny bonuses and long addition in favor of quicker, easier mechanics, hence the double dice-rolling.
A character with Disadvantage could potentially roll 20/20 and crit with a blowgun. A character with Advantage could roll Snake Eyes and bungle a back-stab and sneeze at the most inopportune moment. It's simple, easy to keep track of, and does its job.
Advantage and Disadvantage are set up in such a way that there are hundreds of possible resolutions. 400, to be precise.
With Advantage, your chances of getting a crit are equal to the number of results where you roll a 19 or 20, which means that the other die can be any number that is equal or lower and not change the outcome.
If one die is a 20, the other die can be any number from 1 to 20, so we have 20 possible win conditions for that die, however, the other die could be a 20, and that would be a win condition for that die too, so when we add them, we count the result of 20/20 only once.
19 + 19 + 1 = 39
Rolling a 19 for a crit means any number from 1 to 19 counts as a new win condition, but, like before, 19/19 is only counted once.
18 + 18 + 1 = 37
We add them together to get 76/400 possible resolutions, or 19% chance of a crit with advantage using a war pick. Not bad!
With Advantage, the only way to get a critical fumble and not default to a number higher than 1 is to roll two 1's, which is only one possible state out of 400. 1/400 = .25%, so that's slightly more balanced than flat-out immunity to critical fumbles.
With Disadvantage, it's different. The only way to get a crit is to roll a 19 or higher on both dice, so that's 4 possible win conditions. (19/19, 19/20, 20/19, 20/20). 4/400 = 1/100 = 1% chance for a crit with disadvantage. Sure beats 0% chance amirite?
The chance of a critical fumble is equal to the number of scenarios where a single one is rolled. The other die can be anything from 1 to 20, so that's 20 results for each individual die, save for 1/1, which is in both categories and will only be counted once because of that.
19 + 19 + 1 (sound familiar?) = 39/400 = 9.75% chance, which is less severe than 15%.
The exact workings of the bonuses are unclear. Make sure you understand them by communicating with your DM. Once you have an answer, refer to the section dealing with this.
Adding the bonus to the end of your roll after seeing the natural result ala 3.5 doesn't pack the punch required to substitute for the Advantage system. It's better than nothing, but less helpful than Advantage and less of a risk than Disadvantage.
Trying to make the bonuses stronger by giving them the ability to make a roll of 17 a "natural" 19 and therefore a crit, or a roll of 3 a "natural" 1 and therefore a critical fumble, is too powerful as a buff or a debuff, both for and against the players.
Advantage and Disadvantage should be given a chance. If it helps, roll the two d20s simultaneously to save time.
Show this to your DM by copy/pasting it into a Word document and then sending it to him. Either email it or print it and hand it to him.