How would one say "They should not want to speak here."? That it would be appropriate for them to have no desire to speak.

"Cxi tie, ili devas ne voli paroli" sounds a bit peculiar.

Also, the dictionary gives devi, -u, and devus as options for "should". When would someone use one and not the others?

Thank you.

I would say "Ili ne volu paroli ĉi tie."

As to your second question:
- devi expresses an obligation.
- -u denotes imperative, jussive, exhortative, etc. It denotes always an order, a desire, a wish, etc.
- devus is the conditional form of devi and can sometimes be rendered in English as "should". But not always. For instance "Se mi devus foriri nun, mi forirus." = "If I had to leave now, I would leave."