La 2 et 3 sont équivalentes.

La 1 est équivalente pour le sens, mais plus stylée.

To be honest turn of phrase number 1 is very literary although grammatically impeccabble. If you say it in a spoken conversation people maybe surprised or think you are quoting an author.

In really colloquial normal French, we don’t say “partir” as often as “y aller” (strangely the destination doesn’t matter):

• Je dois y aller : I’ve got to go
• Faut que j’y aille : Gotta go (you often hear people skip the “Il” and we say “faut que …” instead of “il faut que …” Because we are lazy!
  That’s bad grammar but you hear it all the time)

“Nous devons partir” or Il faut que nous partions”, which is completely correct formal French, becomes in ordinary conversation:

• On doit y aller.
• Il faut qu’on y aille.

We use “on” as a substitute for “nous” all the time. Because it’s easier, faster and quicker. Lazy again…