When our house was built, the contractor didn't install soffits. Each
rafter "bay" (sorry, I don't know the terminology) under the eaves has
3 screened 1" diameter hole. I'm getting ready to build a soffit this
summer, and I'd like to ask for some advice:

You should provide as much venting as possible. This will lower your attic
temperatures (thus helping to keep the house cooler), extend the life of
your roof shingles, and minimize ice damming in the winter.

If it were me, I would entirely knock out several of the bird
blocks (the pieces of wood with the 3 holes) and put your
rectangular vents there.

Be aware that the "bird blocks" also serve a structural purpose. They help
prevent the rafters from twisting or tilting to the side. They're required
by code here, regardless of how venting is accomplished.

I would put in the continuous vents as they would better serve
your need attic ventilation.

I agree... I used aluminum "strip vents" I picked up at the local home
center. I mounted mine at the outside edge of the soffit, against the
fascia board. Then I cut the plywood to fit between the house and the
soffit. It's no more complicated than just cutting the plywood to fit the
soffit without the vent. Then I ran a bead of caulk along the edges where
there were gaps or spaces that bugs could get in (Don't get caulk in the
vents! ).

If the bird blocks have screens on them, I would probably remove those to
allow maximum airflow. I would drill holes in the other bird blocks as well
so EVERY rafter bay has air flow.

Anthony