Is there a way to determine your home station without logging out or getting killed?

Hmm. not currently. I'll see about finding a good place to add that.

Yeah, putting that in your Character screen somewhere would make sense.

you currently can find it on your "your stats" link on the game web page

Woodstock

eeerrr... no. That's the current location, not the home station.

You can find on Welcome screen in game (when you select the char)

That violates the condition 'without logging out'...

Technically, you can determine your home station by docking and pushing the button that sets that as your home station. Then you know.... hey, here's my home station! I have now wasted a minute of your time.