Reposting from my other reply: There is strafe actually, even two ways of doing it, using original DOS bindings: < and > or alt + left/right arrow. For me the easiest way to do it without strafe is just to move forward a bit, then go back and wait for dudes to come in from the right. Dealing with imps is really hard since their fireballs are sped up significantly. I tried a bit more and it seems it's possible to actually beat this level properly. You can get other weapons and powerups. It's just really hard with speed mode and nightmare difficulty.

Honestly, the easiest way is to move forward a bit. The imps can't hit you, and the grunts will come toward you, so it becomes a shooting gallery instead of you being in a bullet hell.