chaotiklown,

If you plan to catch fish or animals to eat along your way, you will need a hunting, fishing, or trapping license for each state you pass through - either a resident or non-resident license. Non-resident licenses get pretty expensive. You could easily spend $500 per state for a non-resident license to do all three - hunt, fish, and trap. Plus, you could only take fish or game during the legal seasons. These license and seasonal requirements apply to nearly all land and aquatic species including turtle, mussels, frogs, squirrels, nearly every species of bird. In Indiana where I live, it is expressly illegal to kill any wild animal unless specific permission is granted by state permission, and then only with a license.

As costly as the licenses are, and as restricted as the seasons are, I really think you would be better off to buy food in stores along the way and carry it with you. If you expect to be in one state for a long time, it may be worthwhile to get a non-resident fishing license. And, if you happen to be in a state during a season where there are several game species open for taking, it may be worthwhile getting a non-resident hunting license. Honestly, I can't see snaring providing enough food to justify the cost of a non-resident trapping license.

I do have an idea for you, though. Woodchucks. Or "ground chuck" as I like to call them. They are considered pests in every state that I know of and are allowed to be killed at will with no license or seasonal restrictions (although they hibernate during the winter). I've never eaten one but I hear they are pretty good. They are just grass eating rodents like a rabbit so I bet they taste fairly similar. Farmers along the way will appreciate you killing some of the buggers before they eat any more beans and corn. I don't think you're going to have much luck snaring them or killing them with a slingshot, though. Also, you won't encounter enough to keep yourself fed. But, it may be a legal way for you to supplement your store bought food every now and then.