Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.
There is noting in the stirge stat block that changes this.
The stirge remains in its own square and gives and receives flanking advantage as normal - that is, to creatures on the other side of any adjacent enemy (including but not limited to the one its attached to). Being attached, it will move to remain adjacent the creature its attached to if that creature moves - whether it keeps the same 'orientation' or can choose a different adjacent square is up to the DM.