If I have a plane that weighs 145 ounces with a 27 oz wing loading and an engine-prop that provides 115 oz of thrust at 20 MPH, does this mean the wing is only carrying 30 ounces? In level flight? on an up line?

The amount of thrust you have means nothing to your wing loading. I can take a 50lb brick and give it 1sq inch of wing, just because I can make 50lbs of thrust doesn't mean it will fly.... well.. it might fly but it would be impossible to control and land.

The wing is always carrying 145 oz. in the level,as it falls downward. As the foward thrust increases the speed, the plane or rocket starts to fly " on the wing ". Flight straight up is a no wing deal.

And therefore there is no wing loading. You are trying to understand weight and thrust relationships.

They MAY have the same #'s at some flight conditions.

No, it doesn't work that way. The only time it would work like that is if you're trying to do a 3D style Harrier maneuver where the prop thrust and wing lift sort of work together. The rest of the time the thrust is only used to combat the various sources of drag and pull the airplane through the air to allow the wing to develop it's lift. That's the most efficient way to do it.

Your statement about the 115 oz of thrust at 20 mph bothers me though. At a 27 oz per sq ft wing loading I'm thinking that your stall speed is going to be very close to 20 mph. If you're running a super low pitch prop geared down on an electric and that's the pitch speed then it may not even be able to take off. Your pitch speed needs to be about 20% above your desited cruising flight speed. If it's not you'll never reach the cruise speed and you may not even be able to fly decently. Or at all if the 20 mph is your max pitch speed.

your weight is always acting parallel to the earth's pull, thus perpendicular to the earths surface no matter the attitude the plane is in. if you point your thrust a certain number of degrees upwards or downwards, it becomes a vectored force and must be solved that way in order to know just how much you are burdening the wings

More of a technical point here, but when the airplane is maneuvering ( pulling "G's" ), then the wing carries quite a bit more force than just the weight (mass) of the airplane. For example, in a constant 60 degree angle of bank level turn, the airframe (and wing) experiences twice the normal force of gravity.