The easiest way to differentiate them from their description is looking at the list of gifts : One will give you the necronomicon or a pain branded weapon, and it is mentioned in that screen
But yeah, about trolls and gods :
You need to eat, but it won't really limit your piety gained from Oka/Trog. I don't play those too often with trolls, because Trolls don't need early power from their god (both offer this, when comparing to other gods, bu ta bit less options in the endgame).
My trolls usually end with high unarmed combat and fighting (and either armor or dodging), so what they need a god for are : ranged options, buff options, escape options.
Most characters can use spells for those, but if you don't have a god to help you as a troll, you may easily lack power to get all those online...
One of my solution is going with Qazlal. He offers nice ranged attacks (with small and huge zones), and the summoning power is an escape in disguise (because when you put 3-5 extra targets between the enemy and you, you get more time to flee). He's especially good when you want to wear heavy armor, because he's based on invocations (as most gods), so the failure rate is only based on your invocation. Makhleb is a bit like him (with the whole random-element powers and summons), except his summons are more powerful and his ranged powers either less powerful or more piety-consuming.
On the other hand, there are the magic gods (Sif, Vehumet, and Kiku). All those help you compensate for your lack of magic skill (reducing your failure rate or their severity), and offering you spells. Of course, Vehumet offers much less variety and may not be the best for a troll (he will not help you with (c)blink, switfness/haste, and other utilities)...
Ashenzari may also be considered a bit that way, with her skill boosts compensating you low aptitudes in magic as long as you curse your jewelry. You won't be able to curse your "weapon" if you go for unarmed combat and that may lower your initial piety gain, but as you have less armor slots, you need less curses (and items as gloves/boots/helmets are pretty rare) to be bound enough for her to be effective.
If you play on Trunk, Ru, the new god of sacrifice, may be fun with trolls too, as he's fun with everyone