Farm the hell out of Twitch early on. He's one of the squishiest champs in the game, if not the squishiest, and aggressive play can nerf his farming or possibly even get kills. Don't overdo it, mind, because a few good shots + expunge can kill or cripple another squishy.
Teemo is a hard, hard champ to counter, but not impossible. The only champ I've played that can consistently beat him at his own game is Tristana, as anything he can do for harassing, she can do better. In fact, Tristana is a good counter for all of them - outranges Twitch, has an excellent DoT for fire-and-forget harassment, and has an escape if things go pearshaped (Rocket jump).
The key to ensuring that Eve and Twitch are less of a problem later on is just to give them a really hard time early. Set up a ward in the middle of your lane ASAP and you'll eat them alive. Teemo's blind and poison are tricky, but he's ultimately a squishy that sucks for dealing with more than one champ at a time. Focus him and he'll be in trouble.