Since you aleady oiled the cylnders, I'd check and possibly change the oil, then try a good battery to see if it will crank.
As for cleaning the carburetor, note that the single sidedraft Stromberg has a big rubber diaphragm under that domed cover that will be destroyed if you soak it in carb cleaner (Assuming it's not bad already). Also, any other rubber or plastic parts may be damaged by solvents. And later Strombergs had an electric fuel cut-off valve on the bottom, attached to the main fuel jet. You definitely don't want to soak that part.
Try to check the oil level in the damper reservoir. The early Stromberg damper reservoir was a simple screw and piston assy that unscrewed from the dome. Unscrew it and add engine oil (or ATF for very cold weather) Later Strombergs used an ivory or tan plastic oil reservoir cup on top of the carburetor dome. If you have the later type, be very carefull if you try to unscrew the cover from the plastic cup. It's not uncommon for the whole cup assy to become brittle from heat and age, then crack and snap off of it's plastic thread where it screws into the dome.

Happy Motoring, Mark

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DrDKW