What you've described is a problem with all classes; everyone is better. People run and juke making sniping harder. People are looking behind them, an watching for teammates acting stupid, making spy harder. The three classes you mentioned, however, are assumed to be "n00b classes." Engies just turtle, Pyros just W+1, Heavies just walk around and shoot things. However, these classes have tactics, and as the general population of players get better, these tactics become more important.
1) Engineer: I hear they aren't useful anymore, as players got better but the sentry guns didn't? I also hear that they are really only welcomed in matches above 8v8, and are never in scrims or league play. I hear, too, that Engineers aren't welcome on defense unless they play "offensive engineer." My main question is just how useful are they anymore?
There's a reason why my avatar is a humorous allusion to Engineer
Kinda right; players have gotten better. But sentries are still an aimbot with two Sashas and a rocket launcher. So as a few people have said, it's no longer sufficient to plop down a sentry and a dispenser and jam a piece of paper into the "crouch" and "hit with wrench" buttons and go eat a sandvich.
I'm conceited, so I highly recommend my own post, here:
http://www.edgegamers.org/forums/showpost.php?p=498845&postcount=17
As has been said, Engineer is a TEAM player, even more than any other class. You build sentry guns... to keep other people and things safe. You build dispensers... to heal and equip other people. You build teleporters... to move other people forward.
If you try to play an Engineer all by your lonely, it'll be sad, sad, sad.
Add myself, Captain Calle, and Captain Kraken to your steam friends, and scope out a server with us. I'm not saying we're the best, but if you can Engineer with myself and Calle also Engineering, you'll see what teamwork and sentries can do, even now that spys can sit on dispensers cloaked and scouts can bonk Engies.
2) Heavy: Another class that I hear is completely underpowered. I hear it has nothing to counter but a lot of counters itself? I play heavy sometimes and enjoy it, but I don't want to pour hours into it if it's going to be all useless..
Underpowered?
UNDERPOWERED?
You, sir, have obviously not played on Black Mesa and/or Warpath with some of the pro Heavies we have around. These guys AVOID BONK BASEBALLS and fill people with about 100,000 dollars worth of custom tooled cartridges WHILE EATING SANDVICHES.
The Heavy Weapons Guy is a wall of death... when played correctly. Only spin up when you think you're going to kill things. Have your fists or shotty out instead.
Pair up with a buddy. Medics are the most usual Heavy Buddy, but a Soldier or a Pyro can support you as well. As have been said, the Heavy moves slowly but while causing a lot of pain. A more mobile character, who can help keep an eye around you and flush out enemies while you're attacking is golden.
I've been bonked by a Scout, and had the poor fool walk right into the rocket of my friendly local Soldier.
You're only real problem is snipers, but with planning you can avoid them. Snipers get easy marks with Heavies who W+2 everywhere they go, walking so slowly. Remember, snipers need a charged headshot to kill Mssr. Heavy. Bodyshots won't do enough, and uncharged headshots are survivable in many circumstances. So have your shotty out and run through dangerous areas, and even if you get hit, a sandvich or a medic can solve that problem.
3) Pyro: They look so much fun! Everyone has heard the bad stuff about them... thoughts?
DJSATAN. DJSATANSWIFE. TCVINSKY. CHRIS DA WOLF.
And these are just the ones I have too many killcam shots of.
They key about pyro is that many people BELIEVE he's just W+1. And on n00b servers, you can get away with that. But as EvilDaudilus says, you're a giant walking beacon hen you're flamethrowering, requesting every class to kill you quick.
The best pyros are the pyros you never see... the ninja pyros. To be a ninja, you have to know the alternate routes on all the maps, so you can take a less known path, pop out above people, and fry 'em up all nice and crisp while they still don't know what's going on. And toasted sandviches are the best.
If you want to do W+1, don't do it. Pyro is about sneaking off to the side and ambushing people. My favorite tactic with them is on, say, Badwater Basin, hanging out by the tunnel, waiting for a rush to come through, and then running in and shoving the whole team back out the other end of tunnel with my wall 'o flame.
TL;DR: In conclusion
TF2 is unlike any other game on the market, except maybe TF: Classic, Quake Team Fortress, or Fortress Forever. Unlike, say, Day of Defeat or Quake III Arena, every class is more than just a different character model with a funny looking gun. Every class has it's completely own different playstyle. You can't play a Medic like a Pyro, or a Scout like a Sniper. They're all way different.
If you play on a n00b server, you can rack up the kills with a Sentry, Flamethrower, or a Sasha. This is because the other guys haven't figured out that there is a viable tactic other than W+1 (or +1 for Engineer) and just rush into your waiting death.
Once you get into the real world, however, you have to play your classes strengths against the other classes weakness. Every encounter changes: what you do as a Pyro against a Soldier (flaregun, airblast his rockets, axe him a question when you get close enough) is completely different against, say, a Scout and a Medic.
The combinations are astronomical, and every encounter is different, and there comes a time when W+1 fails, and the n00bs complain that their easy class now "sucks." But it just means they need class based tactics. You can't "n00b tube" your way through TF2 life.
Also as a side note, I just joined Edge Gamers Organization yesterday so thanks for the welcome I will look forward to ubercharging and wiping out their whole team with you all in the future
Welcome! Can't wait to see you around!