No, no, no. Private browsing isn't private like that. Your ISP and network adminstrator (in this case your employer) can still see every website you access. This is usually explained on the "New private tab" on browsers.
You can use Tor and your IT won't be able to see what you're browsing. They will be able to see that you're using Tor, and might get grumpy about that, though.
The use of Tor does show up on the network. The protocol is known and understood, and has been in the detection sets of pretty much every layer 7 filtering product for the last ten or eleven years. What, exactly, is being accessed is largely concealed (but traffic patterns give away a reasonably broad picture of what's happening).
Portable Firefox is hit or miss, depending upon the work environment. It'll definitely show up in file system monitoring, might show up in the logs of the border proxy as an unexpected user agent. The initial download will definitely show up. Removable media might or might not, depending on how group policy is set up.