I had a similar problem. I don't visit my attic often, so by the time I discovered the squirrel infestation, they were v-e-r-y at home. Like some bad sgtar15 skit, these guys had moved into-- get this -- an old Barbie doll house my daughter was storing up there.
The little bastages also had nibbled all the insulation off a ten foot run of romex -- why it didn't start a fire I don't know. They also stink. Attic still smells like squirrel piss a year later.
Here's the challenge. Squirrels leave a scent trail whereever they go. So if you chase 'em out and block the hole, they just follow their urine trail back to the now boarded-up entrance and just eat another hole right next to it.
Dropping them off in the country is really just a slow death. Other squirrels already live there and they'll just drive them out. Drop them too close to home, and they'll find their way back.
You got to kill them, their cousins, their in-laws, any neighbor squirrels that may have visited. I used a live trap baited with peanut butter and the trip mechanism polished to a hair trigger. When I'd catch one, I just upended the entire trap into a 35 gallon trash can full of water. No feaking way was I going to reach into t hat trap and pull out a pissed-off squirrel by hand. Also, I was not interested in eating these city rats -- I watch them climbing out of the dumpsters regularly with god-only-knows in their mouths
I did not seal the hole in the soffit at this point.
1st week - caught 5
2nd week -caught 3
3rd week - caught 2
4th week - caught 1
5th week - caught 0
sealed the hole
and they've never been back