Nice day today (51 Degrees) so I started the engine up.  After running about 6 or so minutes the rightside started smoking a light gray white.  Hmmmm.... checked the oil and it was way over.  I drained the oil and about 6 qts came out, very thin and smells heavy with gas.

Sounds like a bad mechanical fuel pump. The diaphram probably ripped and it's allowing gasoline to dump into the crankcase. That happened to me one time.

Install a new fuel pump and change the oil again. Your engine should be well cleaned out and de-sludged now.Gunslinger2009-03-15 14:37:18

Yup ! I'm with ^
JimG2009-03-15 15:35:10

Ditto the above information and suggestions. 

It will be a parts run tomorrow then.   

I'd have to suspect the fueling pump also, but...it's possible that since your car sits for spells at a time without starting, the carb may be dumping fuel down the intake while sitting. That can eventually put a lot of fuel in the oil. A rich running carb wouldn't be able to dump that much fuel while running, and still actually run.
Looks like time for a fuel pump change.
Soitanly change the oil(and filter) first, then again after running it up to operating temp. For this purpose, you could use a cheaper brand of oil than you would normally use, but go with a higher viscosity...say straight 40wt, high detergent, if you can get it. Then dump that and put it your usual c ocktail.

The fun never ends, does it?

Going alond with what Joel said if not the fuel pump maybe stuck float in carb, hop its just simple fuel pump Good luck