Mass relays are not the only means of FTL, as others have pointed out. They're merely the most efficient way of moving long distances. When you're moving from system to system in a cluster, you're using Normandy's own mass effect FTL drive. As I always say, only assholes quote themselves, so I'll be an asshole and quote the ME1 codex:
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Four thousand years ago, the Mu Relay was knocked out of position by a supernova and lost. Since then, Ilos and its cluster have been inaccessible.
Occasionally, a university will organize an expedition to chart a route to Ilos using conventional FTL drive. These never get beyond the planning stages due to the distance and danger. The journey could take years or decades, passing through the hostile Terminus Systems and dozens of unexplored systems.
As for colonization patterns, yeah, the bulk of the galaxy is toast. There are three basic types of world in the IP:
Homeworlds: Billions of inhabitants, too many to feed and maintain standard of living without massive resource importation. (Earth, Thessia, etc.)
Colony worlds: Millions of inhabitants, self-supporting but may lack heavy industry or R&D capabilities. (Terra Nova, New Eden, Illium)
Mining worlds: Hundreds or thousands of inhabitants, uninhabitable without regular imports of manufactured goods, O2, food, and so on. These worlds supply the resources that feed the homeworlds. (Therum)
What you'd realistically see post-relay is a massive die-off back to sustainable levels. For the mining worlds, nothing is sustainable - everyone dies. For the homeworlds, massive starvation and scarcity - a Malthusian crisis akin to what killed off the drell. Life becomes nasty, brutish, and short as people fight over the leftovers. The homeworlds have all the tech, but they're mined-out - there's not enough to start again from scratch. If they use up what they have, they're not getting back into space on their own.
The colonies fare the best. They can feed themselves and maintain their level of technology (possibly barring a few key industries). They'll certainly lack for brain power (the most prestigious universities and corporate labs are on homeworlds), and the smaller ones will have problems with genetic diversity. They may not be able to get back into space for generations, but they're in good shape to do it eventually.
