1956 Oldsmobile Eighty-Eight

Olds is '56. You can tell by the oval speedometer. It's a Rocket 88, not Delta. I had a 1950 Rocket 88, and it (then and now) drives me crazy when people call it a ''Futurmatic''. That was the automatic transmission advertised on the fender, not the model of car (Buick did that too with the Dynaflow nameplates because an automatic transmission was a big deal back then). The name ''Delta'' wasn't used until the late '60s. In between was the short lived Jet Star nameplate.

The gas door frame I think was a JC Whitney add on, and not stock (but I might be mistaken). I've seen them on '55s, and I've seen them without it.
As for your engine, the displacement is 324 (punched out from the original 1949 303). It has a four barrel, making it a ''Super 88'' (added ten HP over the base engine).
Engine parts are interchangeable from the original 1949 - 53 303s, through the 1959 - 63 396.
Most sheet metal is interchangeable with the '55. Most chassis parts with the '54 -57 models, and GM's ''badge engineered'' counterparts....
Pontiac Star Chief in particular, but also the Buick Super and Chevy Bel Air.
Those spare tire wells were a bad idea, but did add traction over the drive wheel.