[mrgriscom]

I think you're confusing a NEMA 5-20 (120V, 20A) and NEMA 6-20 (240V, 20A). Each has one blade sideways but they're mirror images of each other. T-slot varieties of both outlets are common, which can accept both 15A and 20A versions of their respective voltages. You won't find outlets that can accept both a 120V and 240V plug.

(The standard US outlet "type B" is a NEMA 5-15)

[bluGill]

This house had sockets that would accept NMEA 5-15, 5-20, 6-15 or 6-20. (I forgot the numbers until you mentioned them). It wouldn't be allowed now, but my guess is the house was built in the 1950s.

[cmvincen]

Those outlets existed because pre-NEMA there were competing parallel and tandem bladed plugs/sockets [1]. The plugs you saw were probably like examples 2 & 3 in that link. The parallel configuration became NEMA 5-15P and the tandem became NEMA 2-15P.

The NEMA 6 series is wider than the 5 series and the 6-15P probably won't fit in those old outlets, but the NEMA 2-15P would. . . if you could find one.

1. https://plugsocketmuseum.nl/NorthAm2.html

[mrgriscom]

Ah yes, I have seen those before (quite rare). IIRC they don't have holes for the grounding prong, which should prevent plugging in any modern 240V appliance.