Good news is: They're gone.

Learned a lot about theses little pests though and thought I'd pass on
what I discovered in case anyone else ever has this problem.

First, contrary to what I originally thought, these were not baby or
young grey squirrels. They were full grown American Red Squirrels.
Red Squirrels are common just about everywhere, you just don't see them
out and about as often as the grey squirrels. They are slightly larger
than a chipmunk. The fur is not necessarily as "red" as you might think
but their underbelly is white and they have black rings around their eyes.

I was catching 7 or 8 a day in a HaveaHart trap that I was setting in a
workshop in the attic and then releasing them. Mistake number one.
As others pointed out, they were returning to the house probably faster
than I was coming back from the woods where I released them. Good news
was ... there weren't as many of them as I feared. They were just about
6 or 7 repeat visitors.

I discovered how they were getting in. The four season's porch we have
does not have a poured concrete foundation like the rest of the house
although it does have a stone facade on the framing that looks like a
foundation. The floor framing is insulated but, because it is also
heated, there are gaps in the heating piping from the house basement and
an easy route for the little critters to get in the basement and then
into walls, etc. Plugged the gaps.

I also found a large hole dug under the facade on the side of the house
facing the woods. Filled it in with rocks, gravel and dirt and then
sprinkled some squirrel and rodent repellant everywhere around where the
hole previously existed.

Caught a few more in the trap but now it's been two days that the trap
remains empty and we don't hear any little critters running around up
there or in the walls at night.

Now, here's some info I found interesting and unbelievable:

In Massachusetts and a few other states, it is illegal to trap
squirrels, even if on your property. I think they are referring to grey
squirrels, but the statute doesn't distinguish what squirrel they are
talking about. You can hunt squirrels ... but only during squirrel
hunting season (twice a year). It requires a hunting license and you
can shoot them or hunt them with bow and arrow. Trapping is *not* allowed.

But, get this:

It is also illegal to transport and relocate squirrels or any other wild
animal in this and many other states. Two primary reasons.
First, squirrels are smart little *******s. Once they associate lights
with the potential of a warm, dry attic they like to invade. Relocating
them, regardless of the distance, only serves to transfer your squirrel
problem to someone else. The second reason comes from
tree hugging, animal rights organizations. They claim that squirrels
are very territorial and will attack and kill an immigrant to their
area. The animal rights people are concerned about the stress put on
the poor little creatures. There is actually a licensed animal rights
group who will attempt to "relocate" squirrels under controlled, minimal
stress conditions.

It turns out, if one was to completely stay in accordance with state
laws, the only way to legally get rid of them is to hire a licensed pest
control company who will set traps and then dispose of them by
euthanasia. Killing them after capture is considered the most humane
method of disposing of them because it causes the least amount
of stress on them. However, to be totally law abiding, the property
owner can't do it. You have to pay $1,000 or more to have it done.

I found several articles written by professional pest control experts.
One attempted to test the belief that squirrels will find their way
back to where they set up home by trapping them, tagging them and then
releasing them at different distances from where they were caught.
At three miles, almost all the squirrels returned. At seven miles, half
returned. In one case a tagged squirrel returned after being released
*25* miles from where it was caught.

Best method to euthanize them?

Shooting: Not recommended, either by pellet gun or firearm of any
type. Most residential areas don't allow discharge of a firearm
on your property anyway unless you are located far from any roads
or other houses.

Poison: Definitely not recommended. Stressful to animal and, if
they die in your house it's going to stink for a couple of weeks.

CO2: Not recommended. Dangerous to do and not always effective.

Drowning: This is the recommended and most humane way to euthanize
them. Once trapped, put the entire trap in a big bucket of water. Only
takes about 15-20 seconds and it's all over. Give it a full minute or
two in order to be absolutely sure.

We are now squirrel free.