How to attack in Territory War

Well, with any luck, you've set up a pretty decent defense, and it's time to pivot into offense. The most important thing to remember is to cancel an attack if you haven't killed someone. This means either retreating or force quitting if it looks like things are bad. If you force quit, the opponent will not be attackable for about 5 minutes, but you'll save your friends the trouble of a TM stacked opponent.
The following comps, when used right (and with a little RNG) can take out your opponents' top end teams:
JTR, BB8, R2, +2 (GK, Chopper, Scav Rey, etc.)
Finn, RT, Poe, +2 (RP, Holdo, Rose, Scav Rey)
Nute, Acolyte, Zombie, a low power attacker, +1
AV, Daka, Talia, Talzin, +1 (Spirit, Initiate, or tank)
Rex, Wampa, +3 (dispels, tanks, etc)
UKR,  FOTP, FOE, Kylo, +1 (FOST, FOO, etc)
Thrawn, DK, DT, Shore, Storm (or zVeers lead if you encounter NS with weak zombie).

When played properly, zJTR can take out many EzPz teams, but not all. However, if you do go after someone that is too strong, you can at least take out a tank and EP, which makes it much easier for the next person. I wouldn't recommend going against SiT unless you bring someone who can land buff immunity -- B2 is very good for both clearing taunt and placing BI.

zFinn, RT, Poe, are pretty good against opposing UKR comps, as well as GK/zBarriss comps that don't have HY. You can also make a hole in some CLS comps, but I'd recommend caution here -- it works best if they have a non-rebel tank so that you can prevent CLS's TM gain while you start to pick up steam. Against any comp, you need Poe to be the fastest so that he can get the expose train going.

Nute, Acolyte, Zombie +2 are a pretty well known trick. They can snipe some low aoe comps, for example CLS, Han, R2, GK, Old Ben. The trick is to get stealth on Acolyte, and then she'll never die. Make sure to kill anyone with light AOE early just in case they get a few hits off early. This is shut down by any comp with aoe dispel (like baze) or very strong aoe (like Wedge + R2). It can also be used against some JTR comps, but be careful because R2 can get a lot of turns and his fire dmg can stack up. If you use a weak attacker as your 4th, it will usually attract Han's opening shot, giving your Acolyte a chance to stealth. I'd recommend running Acolyte fast and with high CC to give her the best chance of pulling through. This comp is also very weak to zBarriss, as you just won't be able to kill anyone.

zzAV + zTalzin is generally all you need to handle a top of the line JTR comp. The above trick plus this comp makes Nightsisters a 2 for 1 on offense, and another reason I don't like JTR on defense (easy counter). Similarly, Nightsisters with a weak zombie are an easy target for zVeers comps. Once you land Plague from Talzin, BB8 will spread it to everyone else. If you have zzTalzin (L), this works even better. If you run out of JTR comps to beat, they are quite versatile -- easily handling CLS comps and most Rex/Wampa comps, as well as able to poke a hole in a strong EzPz wall -- as long as they aren't running Shoretrooper you should be able to get enough Plague going to finish a couple people off.

Rex, Wampa, +3 is very good on both O and D. On O, look for CLS or EzPz comps. If you go after Nightsisters, make sure to bring some healing. Enfys Nest slots into this comp very well, and I tend to bring some combination of tanks, dispellers, and cleansers to round it out. Boba is a great addition to this team as well.

A good First Order comp can either be used to poke a hole in (or kill) any of the best meta teams. Strong healing, dispels, and high damage output makes for a pretty strong offensive comp.

Additional notes:
If you see a lone CLS, I'd recommend Teebo (L) ewoks...at G8-10 they can handle a G12 zetaed CLS. Scout, Teebo, and Chirpa's special do a solid job of keeping CLS's TM low, while EE keeps everyone alive, and one of the new guys tags along.
If you see a lone zSavage, I'd recommend Spirit. As long as she has some speed, Savage will just miss her every time, while she whittles away his health. Alternatively, a Poggle lead, GSpy, Rebel Officer Leia team up to one-shot a zSavage. Get a hit in with everyone to stack some buffs on Savage, use Poggle's ability, followed by ROLO's multi-hit, then GSpy's special to OHKO. It's like Boba's execute but on a character that doesn't need much in the way of gear, stars, or omegas (G7-8, level 80, no omegas works).
Lobot (L), IPD, + tanks: you can sometimes manage to kill an EP or another leader with this comp. Lobot is there to make IPD faster, that's it. You can replace him or whatever. +health/defense/etc as lead is fine too. It's finicky and won't always work, but if you get 50 guildmates to try it, some of them will manage to disable a leader. Geared IPD is not required, but the more gear it has, the more likely it will survive to blow up later. Real important: IPD needs to be injured to explode, and needs to have at least one ally still alive.
If you're having a hard time breaking into a heavy empire EzPz comp, consider ROLO (L), Wiggs, +2 rebels (OB, STH, etc.). Someone like Ezra who can cleanse taunt is really good too. Get some damage on EP, then use Wiggs to kill him. If you bring STH, your team will get a ton of TM really fast between ROLO's lead and STH's taunt.