Most ribbon spools just lift up and off the posts they turn on. However, there are myriad other ways that they can be fixed to the machine. Some have nuts that have to be unscrewed from the spool shafts first, others have spring-loaded ribbon guides that are on the inside of the spool and need to be pulled away from the spool before it can be removed.

The closest model I have to your Underwood (Olivetti) is an Olivetti Lettera 25, which like many Olivetti models, uses a metal nut to hold the spool down. It's hard to tell from your photo - an image taken closer to the actual spool would help a lot - but it looks like your machine has some sort of a non-standard spool post, and that there is a pin instead of a nut to hold the spool down.

Have you tried to either pull the pin out from the shaft, or maybe swivel it straight up? 

Also, I wasn't sure what you meant about the ribbon looking "screwy". Could you elaborate a little on what you mean?

 
 

ahh.. got it.. it screwed off..I just have to hunt some ribbon down and should be good to go.