Isn't there a line in Chaplin's City Lights somewhere along the lines of "I will give you a home even if I would have to get a job."
This it the conditional mood. I don't think that you can say "I would should" ;) I didn't even know that it's technically possible in Polish, Wiktionary gives an option for that, but that sounds very strange and unusual.
Also, 'should' is just not as strong as "have to'.
I think simple "should" would simply suggest (mild) obligation here, without the idea of condition. In British English we might say "I should have to find a job", but the meaning of "should" here is the same as "would", and I don't think this is used in AmE.
Does polish have a tense for "I would have had to find a job," or would one just use this?
You could say "musiałbym był" ("musiałabym była" for a woman) to make it clear that it's past perfect conditional, but generally this construction is rarely used in contemporary language - you'd rather just say "musiałbym".
Why is it wrong to say: "I would have to find a work". Maybe "job" is more precise (?)
Work is generally uncountable, "a work" would suggest someone's work (written, for example), like "this work by Shakespeare".
Well, as I understand "I ought to" = "I should", then it's "Powinienem znaleźć pracę" (if I am a man) or "Powinnam znaleźć pracę" (if I am a woman).
This is probably the only verb that shows gender in the Present Tense.