Are female soldiers allowed in the male barracks?

That would depend on the unit commander and the situation. In basic/AIT females were excluded from the male barracks but at permanent party assignments there were no such restrictions as long as nothing was occurring that shocked the sensibilities of roommates etc.

What's the context of the question? Any duty station I've been at there are no male or female barracks - just males and females can't share rooms. I had male soldiers on my floor in the barracks - one next door.

The only place that lodging has been segregated really was basic/AIT and deployment. During deployment males and females in each other's rooms the door had to be open or something. I can't remember exactly.

How, Why, When? Too vague here PV2- During duty hours, same unit, doors open- probably. After duty hours, same unit open doors, maybe. After lights out- NO. In my day no female was allowed pass CQ desk, but we didn't have combined gender training then either. The Command undoubtedly has a barracks SOP Posted somewhere- ask you NCO's