Quake 1 is part of the same continuity as Quake 2 and 4More specifically, Quake 1 is set centuries before 2 and 4. Back then, the Strogg were just a race of Human Aliens who did not yet enhance their bodies with bionics, nor did they form a Hive Mind. In Quake 1 you play as a Strogg: this can be inferred from the Strogg symbol on the military crates you see throughout the allied bases. The story of the game involves Lovecraftian creatures, led by Shub-Niggurath, coming through "slipgates" (teleporters or portals) to invade this dimension. Evidently, the whole experience was so shocking for the Strogg, they decided to research bionics in order to turn themselves into superior beings and repel eventual future invasions more easily. In time, this got out of hand, and bionic enhancements became an end onto itself, instead of a means to reach an end. Alternatively, Sub-Niggurath's influence may have subtley corrupted the Strogg, leading them to take their research too far. Ever notice the military crates in Quake 1? They have the Strogg symbol on them. This means that in Quake 1, the "good guys" are Strogg! And, more specifically, Quake 1 is set centuries before 2 and 3, when the Strogg were simply a human-like race, without any experience in bionic implants yet.
All Strogg are let by a brain damaged computer that started improvising spare partsOriginally designed to destroy the enemies of the alien race that became the Strogg the computer started cannibalising its enemies, its dead and finally its own people in order to 'win the war'. A war that ended hundred of years ago, is still being fought by a insane program that is now harvesting other worlds to re-establish its strength to keep its home world safe. Somewhere along the line it started to forget how to use and develop certain technologies, leading it to use genetic engineering and body parts to create replacement parts. Some of the original Strogg race still exist, in stasis, waiting for the computer to tell them its safe to wake up.