Going to use spoilers as in order to answer this question I'll have to reference (but not attack) the endings.
<spoiler=About the relays> As with all wars, once they're over the civilizations and societies involved in the wars must begin the process of reconstruction. Keep in mind, though, that no matter which ending you choose, technology still exists. There's still scientists and doctors and such that are capable of researching things, but here's at least what I believe would happen as far as reconstruction is concerned for each of the endings.
Control the Reapers: With the Reapers now under the control of Shepard's will, they are no longer the terrifying destroyers of the galaxy. What's to stop Shepard from "willing" them to begin immediately reconstructing the relays? Couldn't Shepard have the Reapers reveal the secrets to building the relays to organics so that they could in turn go on to rebuild society? For that matter, Shepard could likely even have the Reapers help build a new Citadel.
Synthesis: All life becomes united by a common hybrid "DNA" that completely removes the Reaper's purpose for galactic genocide. Now, in this case they're not controlled by Shepard, so they'd be just as likely to wander off into the black void of space as they would be to help reconstruct galactic civilization by helping to rebuild the relays. That said, however, with galactic civilization united in being a bunch of synthetic-organic hybrids, they could still work at rebuilding the relays. If the Protheans could create the Conduit - which is itself a mini mass relay - then that means that all it takes is a certain amount of scientific and technological advancement to unlock the secrets of the relays. It can be done, in other words. Organics can recreate the relays.
Destroy All Synthetics: This would likely take the longest to rebuild society. All the Reapers are dead, so there'd be no help whatsoever coming from them (except examining their remains to analyze their technology). But still, as I mentioned in the Synthesis explination, the Protheans were close to unlocking the secrets behind the relays, so there's nothing that says it's impossible for organics to make new relays of their own.
As for any future ME game that is not a prequel, I'd imagine they could just time-skip ahead to a point where the relays have already been reconstructed and fill in the time-gap with histories and background stories. In the meantime, though, it looks like everyone's going to get to experience the former Quarian lifestyle: living onboard a ship for years if there's no habitable planets for your race in whatever system you got stranded in.
