Hi Chris,
1920s rims are "beaded edge": they have hooks that hold onto a rubber bead on the tyre. The tyres can be stretched onto the rim.
By the 1930s all tyres were "wired on": the rims have a "bead seat" where the bead of the tyre sits. Because there is wire in the bead of the tyre, the tyre won't stretch and the rim needs to be "dropped centre" so that the the tyre can be fitted and removed.
Sounds like the rims you are describing are beaded edge? 20 1/2" probably means they suit 26x3 beaded edge tyres. 26" is (nominally) the outside diameter of the tyre.
Wired-on rims (and tyres) are quoted by rim size rather than outside diameter. Most 1930s rims were 19" ("bead seat diameter" - the ledge where the tyre sits). Then the rim sizes are WM0, WM1, WM2... a WM2 rim takes at 325-19 or 350-19 tyre which is typical for a 1930s bike.
A photo would help.
Leon
[Edit: Should have said that beaded edge rims, universal in the early 1920s, had pretty much disappeared by 1928 - wired-on was a much better plan. Funnily Dunlop had been making wired-on tyres since about 1902!]