In the last century, the ゐ and ゑ characters were eliminated from common use. But it seems like there used to also be a "wu" character that has since been lost. Given that it's a lot harder to find information about "wu", I assume it vanished much earlier.
Around when did the pronunciation and written character for "wu" drop out of use?
The English Wikipedia article on Kana suggests that there has never been a "wu" sound in Japanese.
There are no kana for Ye, Yi or Wu, as corresponding syllables do not occur in Japanese natively[.]
The Japanese Wikipedia article on the sound that would be "wu" confirms this.
日本語では「[w]」の子音と「[u]」の母音は共に/u/であるため、「う」の発音と同じになり、「う」と区別されない。
Because in Japanese the consonant "w" and the vowel "u" both share the /u/ sound, "wu" becomes the same pronunciation as "u" and the two sounds cannot be distinguished.
This page gives information on why there is a kana for "wu" (于).
明治初期の国語教育では「五十音図」優位の見地から、表②のように「[yi]」「[ye]」「于」という文字を無理やり当てた教科書が出されたこともあったようだ。
Because of the "Fifty Sounds" view that was ascendant in Japanese language teaching at the beginning of the Meiji period, apparently some textbooks even forced kana on yi, ye, and wu, as you can see in figure 2.
The Japanese Wikipedia pages on ye and yi seem to give more information.
While the ゐ and ゑ characters were indeed eliminated from common use, there never was a WU character, at least not officially. The wikipedia page linked by Amanda mentions attempts to create a proper equivalent to the other わ行 letters just for the sake of completeness, but this letter (which looked like 于 in katakana but apparently had no hiragana equivalent) had never seen wide use.
The reason for that is that the sounds /wi/ and /we/ were indeed in existence in Japanese at some point of time, so they were naturally given their own letters - but there has never been any /wu/ sound (as well as any /yi/ sound) in Japanese, and thus it wasn't given any letter.
That's not to say such sounds are impossible: English has both sounds (/wu/ in would, /yi/ in year, which most Japanese speakers would pronounce the same as ear). It's just that Japanese never had them. /ye/ is a slightly different story: Japanese does have a distinct /ye/ sound now (written as イェ, though some people may pronounce it the same as イエ). And it also had a /ye/ sound back in the Edo period, but it was actually just the normal pronunciation of /e/ in the beginning of a word (which reverted back to /e/ in modern times). That's where some English spellings such as Yen, Yebisu and Yedo come from.
