Teemo is generally considered a decent counter to most auto attack reliant champs, including the ones you've listed. He does however have a few weaknesses to exploit.

As far as cait goes, you do outrange him, so poke whenever he's at your max range (auto attack is usually enough, teemo has low hp), then if he activates 'move quick' use your net to slow him and gain distance. You should win most of these trades.

Ashe's range is still greater then teemo, but not by much. Ashe is also rather weak early on, her strength is in late game. With both her and yi, the blind is what will kill you, he'll be dealing damage and you won't be. To combat this, fake an attack, rush in, as soon as you see him use blind, back off (use bushes to break line of sight). His blind has a decently long cooldown, so as soon as blind wears off on you, jump on him (ashe's ult and alpha strike work wonders). Without blind, teemo will likely do less damage then you (if equal farm/items). He also has very low hp, so it should net you a kill, or at least force him to back, and miss out on farm.

If you really want to stomp teemo though, grab kayle or an ap burst caster (annie, brand, anivia etc) :)

Hope this helps!