From a technical standpoint:
yes they can monitor all network traffic on their equipment. This includes all web/email/torrent/etc traffic going in and out of your personal computer going through the work wifi/ethernet. Some VPNs are susceptible to what is called a "man in the middle attack" which your work would be able to use, to see the un-encrypted VPN traffic. However that is a lot of effort and they may just block that type of traffic. Also they would have to hack in to your PC to see what is on the screen, and that is unlikely they would bother.
From a legal standpoint:
This varies from country to country, and in some places depending on company policies and agreements signed. But I'm going to guess that most places will have something in place to ensure their staff are productive, and not doing anything illegal or damaging to the company reputation, without the technical equipment and services costing them too much.