I noticed that I can connect to my wireless network even if the router isn't connected to the internet. Does this mean I can get a secondary router which I won't connect to the internet and set up a wireless network for file sharing with that offline router? Would that work or would the router have to be connected to the web to allow traffic between my comps?

Nope, not being on the internet would just mean you can't share with the internet. You could easily share stuff between whatever computers were hooked up to the network.

If you just wanted a way for wireless comps to share files, you would make an ad-hoc network (similar to connecting 2 comps witha crossover cable) but if you had wired and wireless you could jest get an acess point, I belive linksys makes one that looks just liek the router except no WAN port. So like it has a 4 port switch on the back to wire your comps in and also provides wireless acess.

If you just wanted a way for wireless comps to share files, you would make an ad-hoc network (similar to connecting 2 comps witha crossover cable) but if you had wired and wireless you could jest get an acess point, I belive linksys makes one that looks just liek the router except no WAN port. So like it has a 4 port switch on the back to wire your comps in and also provides wireless acess.

Linksys WAP's typically just have one port on the back.