New is probably one of the more academically inclined colleges. Having said that though, most people are pretty keen to have a good time as well. So generally they're pretty well rounded people. I'm guessing you know about the no alcohol inside college rule, which means that the stuff which goes on inside the college doesn't revolve around alcohol (although there are plenty of opportunities to go out if you want to).
As for the religious stuff, I wouldn't say it's ever overwhelming. It's there, but you can participate in as little or as much as you like.
As for the rules they're all pretty standard stuff to do with harrassment, disturbing other residents (i.e. keep noise down after 11 o'clock), etc.
In regard to the food, don't expect to have your tastebuds blown away. It's edible, you won't get sick from eating it and it meets nutritional standards. Eurest has the catering contract for New College and the Kensington Colleges (and probably some of the other colleges as well), and I'd say New and TKC pay similar amounts pp for food (given the similarity of their fees), so I'd say it's pretty much on par with the other colleges.
Clothes washing will cost you a dollar each time (driers are free). For some people that'd only be $10 a year - but I wouldn't really advise that.