Is it possible...

[Stapled]

To tell if and who is downloading on your network?

[Elliot]

Yes, go to your router config page. http://192.168.1.1

It should have a log of every device attached. And from there you can enable advanced logging of everything they do.

[GAMEchief]

Router config page IP address subject to change with each router.

[Stapled]

Yes, go to your router config page. http://192.168.1.1

It should have a log of every device attached. And from there you can enable advanced logging of everything they do.

My router is balls and lacks a lot of functions, including logs.

[Elliot]

My router is balls and lacks a lot of functions, including logs.

dd-wrt might be an option.

[Omlett]

You can deactivate all wireless connections if its starting to annoy you.

[323]

dd-wrt might be an option.

This.

dd-wrt is a great custom router firmware, and is installable on most routers. I got a router out of the trash, and transformed it into a wireless bridge using dd-wrt so that I could have great signal strength anywhere in my house. It also has a lot of great functions you wont find on some normal router firmware, and is extremely easy to use and has the functionality that you're looking for (Seeing attached devices and such, you can even configure your network so that it has no password, but you can't actually access the internet on it unless your MAC address is on a whitelist. That's how my router is, and it's helpful because people go "Yay an open network I can torrent stuff on" and they connect and everything, but they can't get any websites to load or any incoming or outgoing connections. Keeps the neighbors off.)