Network oddities

I'm at a college apartment complex that allows its own routers in tenants' rooms. I'm assuming there is a main router/gateway somewhere on site that filters content/ports/services as the usual bittorent and IRC and now Tor are blocked, in addition to allocating near-dialup speeds per user. Just like a university network but minus the 7MB/s

IT noob here, by the way. Are there some network tools that can point out what exactly is being filtered? I can't even use wget to download a linux iso from legal sites without it bitching about http header errors and connections being reset by peer.

Is putty/ssh able to 100% bypass all this bullshit? Tor worked nice for about a month until the WAN ip switched and now I think they have those exit nodes blocked, and any http proxy is just shit/blocked by the gateway

Time to get a VPN I guess

tl;dr network tools that tell what ports/services are blocked on my apartment's network and good cheap VPNs, plz

You could just do a internet scan which would take a long ass time, but also you can just use proxies to mask your general IP in order to access otherwise blocked headers, IPs, etc.