1988 Honda Accord DX does not want to heat up, idle, or take off.

[CharvelM2]

My 1988 Honda Accord DX has 168k miles on it. Recently, on one or two
occasions the car has started but due to the cold New York weather has
decided not to heat up. Eventually the idle grows so poor that the car will
just stall out and attempting to restart the car after this is basically not
happening. However, it is not the thermostat that causes these problems
as I have replace that along with other parts that I felt might have been
to blame for this such as the spark plugs, wires, the distributor cap, rotor,
and the radiator.

I have also noticed that the car's exhaust smoke is white
with a hint of blue if the car is revved. As I said before, I replaced
the spark plugs and wires recently (about a week ago) but today
when I opened the hood to look around it appeared that oil was
leaking down the engine and a removal of one of the sparkplugs
verified this as it is charred black. I will enclose pictures below.

Does anyone have any words of troubleshooting wisdom for this
situation? I just hope that the car wont have to be laid to rest
but putting money into something that in the end would not be
worth it is out of the question for me at the moment. I also dont
want to spend a grand sum of money only to find that the offending
part was an old gasket or O-ring of sorts.

Help please! and thanks!

[POS carb]

do a compression check. If all cylinders are about the same put some new plugs on it. Check that the choke is opening as the car warms up. You may want to try jamming it open a bit