I've said this in other threads, but I think Bogdanovic has trade value, he's aging and he's in the last year of his deal. If the Jazz decide they want to get younger, more athletic and more versatile defensively, Bogdanovic is a pretty obvious trade candidate. The Jazz reportedly almost traded Joe Ingles last offseason for the same reasons.
I'm not sure if Conley has much trade value on his own, given his current contract. He would need to be moved as part of a larger package. Some Knicks fans would be willing to trade Julius Randle for Mike Conley, but that's only because they view Randle as a worse contract. I think the Jazz would probably like to move Conley, but I could see Conley coming back and playing reduced minutes if the right deal isn't there. He could also get moved at the trade deadline if Butler and NAW are coming along.
I think the Jazz like House and would like to bring him back, but it will depend on his market.
I think the Jazz are stuck with Gay, unfortunately. It's going to take at least a pick to get off his contract. He's the new Ed Davis. Maybe he gets included in a package deal.
The real question is whether the Jazz want to keep Gobert, or change the direction of the team. If it were me, I wouldn't be in a hurry to trade Gobert unless someone just wowed me with a trade proposal.