I'm not going to go too much into it as Adrienne is Far more experienced than I am in this, but I can give some information to get you started. We're going through something somewhat similar and I'm going to be digging through the archives momentarily for answer of my own. :)
Thank goodness you have roommates! That means extra trainers. My suggestion to get your started is this. Have your roommate with their respective dog (and I would try this one dog at a time). The larger dog may be easier because Dachshunds are kind of . . . jerks (that's who I'm having issues with). So have your roommate with the larger dog sit with their dog and, at a safe distance, walk your puppy past them. Every time the larger dog doesn't react, or reacts Positively, have your roommate give him a treat. Rinse and repeat. When the larger dog consistently doesn't react (or reacts positively) at that distance, shorten the distance and do it all over again. It's boring, trust me - btdt with Momo and his food aggression. The first week's training was me touching his bowl and giving him a treat to form a positive association with me touching his bowl. <yawn> A little boredom for a peaceful household is worth oh-so-very much, though. Omg, the fights, break-ups, and resentment that can result between the humans when it comes to their dogs . . .. Eventually the older dogs will form a positive association with the puppy and will Want to have him around because he is the bringer of yummy treats.
If the other two dogs tend to lunge it would be best to have their collars on, and probably a leash, for better control. Eventually those could be phased out (dogs are weird - they may also associate leash + puppy as a good thing and no leash + puppy as bad).