340 engine oil consumption ???

:help: My son's High School / early college project Got a 1970 340 engine that was sitting idel for 4.5 years as car belonged to my son who died of cancer @ 24. And I'm no motor man. After getting the bent push rod fixed and engine fired up. Its now using aprox. a quart of oil in less than a 100 miles. It has occasionally smoked but for a very limited time. Exhaust tip right side is wet. (looking from front of vehicle). I'm asking the "MOPAR" experts as to what I need to do.
Some info I've learned about the engine. That I've located from his Duster file.
- Orginal Motor- numbers match (balanced)
- X. Heads , angle valve job, Ported, combustion chambers polished- (something TRW valve springs -single w/ damper) same as stock
-Pistons - TRWL2316 F - .060+ - Stock rods full floating pistons.
-Crank- foraged steel standard mains + rods (improved wedage tray something)
- Double roller timing chain
-Cam- P.3690213 284-284-60degree- .471in 474 ex (street hemi grin purple shaft)
- Oil pump - high volume (25% increase)
-Headers- Black Jack
- Clutch Stock H.D. 11" for 400 CU IN motor
-Fuel pump - Carter high volume
-Perfomer Intake w/ 67 400 CU In manual transmission carb.

Guys I'm total lost in this don't know where or what to do on oil consumption as not leaking, no stains on carboard under car. Only thing seems to be greater in hot weather. Currently have just over 1000K on last oil change using "Citgo 10 W 30". Should I be using straight oil? Heaver Grade?
I wish i could ask him.
So any help directions; NO I'M not going to sell it. I've given it away to his best friend but he doesn't know it yet. Some day he'll be driving it, but for now i'm enjoying something that i never had when i was younger.
Also can some one inlighten me on horse power if possible with the info i've been told about this engine..
Car has 4 speed A-833 / bench seats/ sure grip 8 3/4 3.23 :1
Thanks ever so much.
"Frustrated" and Sad.. But got an angel that is always with me..