Tukukkk

I've made a character that is going to eventually put 17 levels into Monk's Way of the Shadow and 3 levels into Rogue's Assassin.

I was looking at some of the abilities I get for attacking, such as Stunning Strike and Sneak Attack. Would it be possible to use both of these abilities in one attack before I used my extra attack? (Gained at 5th level, Monk).

I've looked and I haven't seen anything related to the question. Is it possible?

Can a multi-classed Monk/Rogue use Stunning Strike and Sneak Attack before using the second monk attack?

Yes, though it requires a melee weapon attack with a finesse weapon that hits. So it won't work with either a ranged weapon or unarmed strike.

Stunning the target is also a good way to gain advantage in order to apply Sneak Attack on a second attack.

Yes. Abilities like sneak attack don't consume any action resources (like needing to use your bonus action etc.) so you can use as many together as you wish. Some have a limited number of uses per turn (eg. sneak attack) but that is the only limitation on them. You could even add some paladin levels and use divine smite at the same time as the other two.