SCCA Classing question..

V8, right?

If the car is genuinely SCCA Solo Stock legal, it would fall into F-Stock. The car isn't classified (can't imagine why no one asked for it to be), so it falls under a "Not Otherwise Classified" catch-all for V8 sedans.

Cage, gutted, lightened, exhaust, race seat, etc.?   What exactly have you done? 

--Rob
(Local SCCA classing expert - no seriously - I was solo chairman and the Philadelphia Region's President)

He posted about this before and if I remember right its his daily driver 78 olds cutlass holiday, so I'm guessing full interior no cage.

Honest answer:

No cage.
Not lightened with anything that wouldn't have been avail on factory order sheet - Does have aluminum hood
Original factory bucket seats
Exhaust - true dual with 2.25 pipe, no cats, and Summit H-Pipe.

Only things that would have never been available as THIS car left the factory:
1. Hurst Dual Gate shifter - Taken from a 79 Hurst Olds.  Fit factory console, looks VERY factory.  Replaced T-Handle factory shifter.
2. Holley 600CFM 4BBL Carb - Originally equipped with a Rochester 4BBL
3. 235/60R15 tires - Original was 205/70R15
4. Exhaust - was originally single with 2.25 pipe.  Never offered in true dual.
5. Tachometer
6. Aluminum hood - Available on OTHER 1978 Delta 88s, in fact that is where it came from.
7. K&N Air Filter - we all know a K&N adds like 50 HP just bolting it on.

Rear springs are Moog Cargo Coils, but they aren't staying.  Front springs are original 1978 Delta 88 springs.

It is a 350 Oldsmobile Motor (5.7 liters) - factory stock.

Full street tires.  No questionably street tires.  I drive it to the track, drive it home, drive it to work, and drove it 4 hours one way on the same tires.  Firestone Firehawk Indy 500 raised white letter tires.

So these three things are not SCCA Solo Stock Class legal.  (The springs aren't either but you said you were swapping those)

Because the hood is a part from within the Delta line, and the shifter and carb are allowed under the Street Prepared rules, you would be in the E-Street Prepared class (ESP class letters). 

That said...  The odds are that no one is going to say anything locally if you run in FS or STU especially since the car is old and you are on street tires (not 200 treadwear racing tires).