Zerg organisms are really not at all similar to those of humans, they do not need to breath oxygen, and well, they really don't breath anything at all. And due to their nature they have adapted to space's vacuum and managed to simply 'slide' thorough all matter, essentially enabling a sort-of hyperspace interstellar travel, similiar to protoss with portals.
edit: Obviously this has a-lot to do with their psionic capability, basicly I'd guess that their psionic capability is not only on ground 'zero' level, but actually interracting with subspace, thus allowing them to create actual hyperspace windows with their mind, and seeing as they don't need oxygen to breathe, well. ^^'', blizzard just didnt really take everything in account.
If shrimp can cause mini nuclear reactions by chance, I don't doubt the zerg master race can fly in space.
As said before, it's probably their natural psi powers. However, the animals that eventually became mutalisks were flying before they were zerg
How? Not explained as far as I know, but this is pretty common in scifi and the technobabble isn't hard to make up.
EDIT: Shrimp reference
Well, They have a way to propel themselves into space. It would make sense if they evolved, they being leviathans, some form of solar sail wings. Not exactly sure. Quoting Stracraft Wikiw: "Despite being a race with no use for technology, the zerg still maintain the ability to travel through warp space, as they can open large gateways into warp space. The power of these gateways was immense, able to even pull zerg off the surface of a planet, emerging at their destination. This process was highly accurate, the zerg emerging right over a planet, so accurate in fact, that it appears the zerg could enter real space within a planet's atmosphere, as no traces of atmospheric entry (eg. a buildup of heat due to friction) ever being observed. The Overmind had the ability to open these warp rifts.
The zerg are still able to travel quickly and effectively through warp space after the death of the first Overmind using behemoths and leviathans. Infested Kerrigan was able to open wormholes as well."
37 + (3*7) + (3*7)W/L/Death count: Wolf: 0/1/1 | Mafia: 0/5/5 | TPR: 0/2/2SK: 0/1/1 | VT: 1.5/3.5/5 | Cult: 1/0/1Legendary Overlooked