I'm curious what size the drop between utility pole and top of the service
entrance is. I'm *not* taking any actions based on answers given.

Single family home built in 1957. There's a solid support / neutral with
green oxidation so I presume it's solid copper. I checked with a magnet to
see if it might be copper-coated steel but no magnetic attraction. It's
..15" thick. The two "hots" have smooth shiny black insulation with no
writing that I can see and they are .30" OD. I believe them to be solid as
well. Does the neutral have to be the same as the hots (no relying on the
ground to carry unbalanced)? I'm guessing 6AWG although I see a listing
for 7AWG but I've never heard of odd sizes in practice.

There are two main breakers: A double 30A feeding the dryer outlet
directly and a double 50A feeding the rest of the panel.