There are some really good answers to your question, but I want to throw out a couple more thoughts.
You asked, are 5th Edition D&D PCs too strong?
Maybe, maybe not.
Maybe it's your PCs
Maybe it's your PCs are overpowered. First of all, there's nothing wrong with overpowered PCs. It's what they do. It's what they want to do. They want to run in there and kick some monster butt. That's a good thing. But if they're overpowered, you gotta take that into account.
Are the PCs using standard stats? Or did they roll their own? If a PC starts with a stat above 15 at character creation, then with racial bonuses and ASIs by 4th level you can be dealing with a character with a 20 stat.
Have you made house rules that favor the PCs? For instance, relaxing multi-classing restrictions, weapon restrictions, or spellbook restrictions. That can up their power.
Are you (or the PCs) playing fast and loose with the rules? PCs may be interpreting the rules in the most favorable light, or not taking into account limiting factors, such as spell components or the action economy.
Don't get me wrong, I loves me a high-powered PC. You just have to take that into account.
Maybe it's your monsters
You don't say which particular monsters you were using. I took a look at your final encounter, 1 CR 8 and 3 CR 3's. For representative monsters, I chose a Chain Devil and 3 Barbed Devils.
By the DMG's encounter estimation guide, I think the numbers come out pretty reasonable for your party, especially later in the day, after they've been softened up a bit.
But are the devils playing to win? Because the PCs definitely are.
If they're the big encounter of the day, they need to be ready to rock. Do the PCs got tricks? Then the devils need them too. They can't just run out there and start swinging, they got to strategemize.
In the case of the devils I listed, they aren't super-powerful. They aren't going to last long toe-to-toe with your heavy hitters. But they ain't stupid. And this particular little stretch of dungeon is THEIR turf. This ain't their first rodeo. They didn't get where they are by getting sliced and diced by the first PCs that came along. No sirree bob. And what's more, these particular monsters got some specialities. These particular monsters are IMMUNE to fire damage, and they gots telepathy and devil's sight. Your PCs would chop these guys into pieces under normal conditions. But in a room filled with flaming oil and magical darkness and silence, it would be a different story altogether. Just those three features could turn it from yawnsville for the PCs to a TPK. Heck, just one of those three features would turn things significantly in favor of the monsters. Let's see how your barb likes it when he is taking fire damage per round because he's coated in flaming oil, taking dex saves to keep his footing, and fighting in darkness and silence. Suddenly it's barbarian barbecue.
You might say, that's not fair, the MM didn't say that devils can create magical darkness or silence, or have flaming oil. That's true. But it says they have devil's vision, telepathy, and fire immunity. They have average intelligence. They're going to try to use their innate abilities.
A Time to Reap
Are your PCs ready to die? Are you ready to kill them? I mean that seriously. What happens if you kill a party member? There's no right answer, there, it depends on your campaign. For me, I try to avoid a flat-out PC death, but taking them to zero is a goal. Dropping a PC and forcing them to drag his sorry ass out of the fight and regroup is good. Heck, it's great. And death is a possibility. There is death-reversal magic available. It will cost, though. It will cost the PCs dearly on gold and plot to bring back even one PC. And that PC will be forever changed. Some campaigns, PC death, no resurrection, is part of the deal. Other campaigns, PC death never happens.
Are your monsters ready to die? Because they shouldn't be. Depending on the monster, when things go bad, they should get the heck out of Dodge. Maybe they grab their fallen buddies and fall back themselves. Maybe they throw a weaker monster at the PCs to buy escape time. But when the going gets tough, they should get going. Warn the boss monster. Get some reinforcements. Cause it's the peecees and the monsters know what happened the last time they got in here.
To answer your specific questions:
"In your campaign do you find that the PCs are strong compared to the CR/xp ratings of the encounter?"
It entirely depends on factors beyond PC level and CR/xp, particularly extra abilities, prep on both sides, and environment.
"Would it help if I stopped estimating the CR of encounter and stuck to the DMG more rigorously when designing encounters for my group of 6-8 PCs?"
Maybe that would help. But try overpowering your encounters then pulling punches. In my devil example, if the chain devil had nothing but a room full of chains and a rock in a bag with magical darkness, or maybe a ring of spell storing with one fireball on it, that would give the devils a chance to seriously bedevil the PCs without an auto-TPK.
"Am I correct in assuming that the CR ratings for monsters as given will not provide a significant challenge to the PCs going forward beyond level 4 and 5. Will I need to increase the power level of the monsters, or make other things like terrain to not be in their advantage when designing encounters for my group of PCs?"
The CR ratings are a start. Given a balanced encounter, the monsters got to use everything available to them though. Otherwise you need to bump up the CR.
"Is what I am seeing a function of adding additional PCs beyond the first increases the power of the party in a non-linear fashion or more a function that the PCs work well together?"
Adding PCs definitely has a network effect. And they are working well together.
Reading your adventure description, I think you've got a great base. You're clearly putting some real effort into it, and I'm guessing everyone is having fun.
In dealing with the numbers when designing encounters, you might want to take a look at Kobold Fight Club. I am not all that good with it, but it is an awesome tool. That's how I came up with the devils in the example.
Speaking of kobolds, if you haven't read it, you might want to read Tucker's Kobolds:
Here's my final advice, if you really want to give your players challenging encounters. Take it with a grain of salt. It heavily depends on your group and your play style:
Keep piling it on. Keep piling it on til you drop a PC or two. The day they get their butts kicked and drag a couple of unconscious characters or maybe a dead one out of that monster-infested #@*% pit of darkness will be the second-best session they ever have. The best will be the next time, when they come back and this time they mean business. This time, the characters are pissed and out for blood, and the players are gleeful. This time, the monsters are going to pay. Houyah!