Is it white white smoke? or does it have a blueish tint? Assuming all else is in order, you might want to check the seals on your Carb. Is the dash pot holding it's oil? There's a tiny o-ring that goes on the fuel mixture adjustment screw that hardens when it gets old. If it fails then you'll end up with dash pot oil being sucked into your intake and end up burning oil.
You mentioned the float earlier. The float on a Stromberg carb is on the bottom. I do not suggest attempting to adjust it (the float) on the car. The only way I've been able to properly set the height is to remove the carb from the car, drain the bowl, and invert the carb on a work bench. There are 6 screws that hold the cover on the bowl.
Other things to check while the carb is off the car. The dash pot spring, if it's too weak your mixture will end up too rich when you press the accelorater. Due to the lack of resistence the piston will "float" up too high enriching the fuel mixture too much. Combine a weak dash pot spring with a bad dash oil o-ring seal and you have a combination that'll seemingly be ok at idle but way too rich while driving. No oil in the dash pot will leave the piston undamped and allow the piston to rise much too quickly.
Another thing to look at is the fuel mixture needle (it's on the bottom of the piston). Sometimes the needle assembly can disassemble itself and the needle springs up inside the assembly about 1/4 of an inch. When this happens you can never lean the car out enough; it will always run too rich (I had this problem when I bought my car, a 76 B). You can fix this by either ordering a new needle assembly, or pulling the needle assembly out of the piston and replacing the pin that holds the needle in its assembly. Be careful though. The needle is held in place by a spring under it and a pin above it. If the pin is broken, the needle can launch itself and put an eye out... or worse cause one of the smaller pieces to get lost! The pin in my assembly is really small, but I managed to fabricate a new one out of a straight pin.
If water is finding its way into your carburetion, well that can only be one thing that I know of... the choke. I'm not sure how to fix that as my car was converted to manual choke long before I bought it. I'm considering going back to an auto choke ZS, but haven't set my mind to doing it yet.