So last night my guy was running around with DR 3/Cold Iron.
Some stirges thought I might make a good meal. One of them hit me and drained some Con.
Neither I nor the DM knew how to square this with my DR, so I leave this to you guys to answer.
Ran into this once. Stirges drain CON by playing mosquito and drainng blood.
So the question is, can they drain blood if they can't penetrate you DR 3 skin?
The key was that Stirges do actual damage first, then drain Con. Our DM ruled that unless they did enough base damage to penetrate the DR, they couldn't drain any blood, hence they couldn't drain any CON.
Note that this was when someone Summoned a Stirge Swarm on some Titans, so the ruling was flavored against the PCs.
Luckily for you, Stirges do CON damage, they do not drain it so you should be able to heal it with just some rest.
But the Stirges don't do damage at all...they just attach