My dad passed away a few years ago. He used to say that when he lived in a different city he had a 401k there (he wasn't with us then), however I don't know who was his employer. I tried asking IRS and SSA and they won't help... How can I go about finding out where he worked backed in the early 80's?

Maybe (?), a Freedom of Information Act (FOIA) request to IRS and/or SSA, or similar request to the State Income Tax division (called Public Information Act (PIA) in some states.
These agencies have umpteen pages of requirements and hoops to jump through. No guarantees.
SSA's FOIA policies: Freedom of Information Act (FOIA) at Social Security
Also, watch the state comptroller's office website for notice of abandoned funds which will likely take 3 or more years to show up.
No guarantee.

Have you talked to whomever was the executor of your father's estate to see whether this was investigated, or whether he or she went through your father's financial papers to make sure all accounts were properly accounted for?

If he had a 401, they should have been sending at least yearly statements. Who was checking his mail, for the year after his death, where is his prior years tax papers, it should be listed.?