I can certainly understand your confusion. When I first came to OA I bristled at the word God, especially when I heard people refer to anything more specific. But I also felt that I really was a compulsive overeater, these people seemed to have an answer and nobody tried to get me to go to any church. Then I realized that the Steps said things like "Power greater than ourselves", well that was OK. And they said "God as we understood Him". I did not like the "Him" part but it really did not tell me what I had to believe.
So I started to think about what it really was that I did believe and I knew that there was power or spirit at the beach and in the mountains that I felt close to when I was near those places. I found that no one tried to make me believe anything; they really only talked about their experience and that felt just fine. Once in awhile there are some people who do try to push their religious beliefs onto others in OA but most of the time they do not. I know that sometimes when I tried to explain some of my "nature" ideas to others who were Christians they got kind of uncomfortable around me.
To me a religious program is something that sets forth a specific set of beliefs and there is NO where in OA that does that. OA has some practices which are similar to some religious practices, such as confusion. But therapy might be like that too. But nowhere does OA try to make me belief anything really specific about God. I personally know Christians, Jews, Muslims, Buddhists and believers in the power of the universe who work a 12 Step program. So by my definition OA is spiritual rather than religious. I have a much closer connection with God of my understanding today than when I first came into OA.
My main suggestion to you would be to give it a try - what do you have to loose? I know that no one could convert you to any thing you don't want to believe so it should not hurt you to go and see if it makes sense for you. More than anything I hope that you can find a way to have peace with your food and your weight.