How old is he? What do you know about his background? Using food rewards in training is usually an effective way to teach new behaviour but it is important to move to a variable schedule of rewards once the dog understands what you have taught him and has it on cue, i.e. will do it when you ask for it. If he does not know when he will be rewarded but that there is a chance it will be this time, he is more likely to comply with your request.
Having treats visible is a mistake, IMO. If you are working on something in your house vs when you are out walking, then don't even have the reward with you. When you get the correct response go and get whatever you are rewarding with. That way the dog doesn't refuse to work when he knows you don't have the goodies on you. (make sure you "mark" the correct behaviour either with a clicker or with a marker word when you get it, so he knows what he did to gain the reward).
In what context does he wreck his bed and blankets? When you routinely crate, or when you crate after he has been acting out, digging the couch, whatever?