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The typewriter whose image you posted appears to date perhaps from as far back as the late nineteenth century.

No, ours looked just like this, and it was not an antique in the 1950s-60s. Ours was maybe 20 years old, give or take, at that time.

I recall using the letter “l” for the numeral “1” on a portable Royal manufactured about 1950, but never had to use the letter “O” as a substitute for the numeral “0”.

Well, I did, if the other three typewriters in the house were being used by someone else who was older.

I can’t even recall the name “Olympia.”

I do. I won't say for sure that ours was an Olympia, but I do recognize the brand name.

Wikipedia says that it was a German brand.
http://en.wikipedia.org/wiki/Olympia

http://commons.wikimedia.org/wiki/Category:Olympia_Typewriters
This page has a photo of a 1964 machine that does not have a zero.

As I said, ours looked a lot like the one in the photo.

Ah, so you had a German typewriter. Judging from the chronology, it was very possibly manufactured during the Nazi era. Ugh!

The German make probably explains the transposition of the "X" and "Y" keys, which, as an educated guess, occurred because the letter "Z" is more common than the letter "Y" in the German language.