Can anyone tell me what body style this is? My wife inherited about 6 guitars and we can't find anything like this on Google. There is no serial number that I can see.

Thanks for sharing the pics! I’ve never seen one of these and it’s a damned cool guitar.
Specifically an SC 550, as I posted in that link. It's in beautiful condition too. There's a project on ebay with no hardware going for $400. This is probably worth a bit of money.
Gibson RD Silverburst w/ Lace Dissonant Aggressors (SOLD)
Electra Omega Prime Ceruse
Fender Franken-Jag Bass

Amps and the like:
Laney VH100R
Seismic Luke 2x12
Dunlop 105Q Wah
Gojira FX 808
Line 6 M9