Unfortunately you have to deal with Continental (or NW if they are acting as CO's agent at that airport). According to policies at all the airlines, whatever airline carries you to your final destination is responsible for all baggage claims, investigations and delivery. So US is out of the picture, as is UA, even though arguably it was UA who caused this mess. Behind the scenes, CO will deal with UA and US as needed.

US is very firm about this BTW. I had a similar misconnect going US to UA where I ended up being rerouted on AA as the final leg. A US GA in DFW (the misconnect point) kindly tried to intercept the bags as they were unloaded, radioed down to the ramp to route them over to AA. But when I got to DEN (my destination) and asked at US to check if US had successfully pulled them and sent them to AA (after they never showed at the AA carousel) I was firmly told that US wouldn't do anything. I also found out that US has absolutely no bag tracking, no scanning of barcodes or anything like that - which probably explains why CO is having such a hard time getting information from US about their whereabouts.

AA did get them to me a day later, and it turned out they ended up on the next morning's UA flight DFW-DEN.

BTW, paragraphs are your friend.