Can admins monitor my activity locally even when I use a VPN?

When you run VPN, the bigger network just sees an encrypted stream, with no way to identify the contents of individual packets. Assuming the machine you're using isn't compromised (and I don't imagine your school IT department has that kind of capability), your activities are quite invisible to them.

Thing is, they can see that you're hiding your activity from them. If they're serious about filtering content, sooner or later they're going to tell you to cut it out. Then again, their use of a simple-minded content filter suggests that they're after the appearance of Proper Adult Supervision, not the actual fact. So you're probably fine, as long as you don't go around boasting about your ability to bypass the Great Firewall.

If this is your personal computer, and the school has not had any access to it:

• The IT staff can see that there is traffic, and that it is encrypted

• The IT staff can see that you're connected to VPN Reactor based on the endpoint of your connections from their networking equipment's point of view

• As long as your computer is routing all traffic over the VPN, the IT staff cannot actually see anything you're sending over over the network

• All traffic going over the VPN appears as if it's travelling to the VPN, from the IT staff's point of view

If this is a school computer, or there is some sort of school software installed on your personal computer:

• The IT staff could potentially be logging every keystroke you type, taking random screenshots, or remotely viewing your desktop, all without your knowledge

With all of that said, you'll want to make sure you're not violating your school's policies, as it may be against the rules to circumvent their security measures. If you're not worried about that, Isaac's advice about staying under the radar is probably a good idea.

They can set up transparent proxy. And they can see that many requests (megabytes) is going to single domain / ip. So, they can view what that domain/ip is and block that. But they cannot see what data is sending to that ip/domain.