Oxen is a rare exception in English where it is the only common English word that retains the original Old English plural ending -en. (Note: Children and brethren are formed a bit differently, please see the note at the end.)
Etymonline has this explanation for oxen:
plural of ox, it is the only true continuous survival in Modern English of the Old English weak plural (see -en (1)). OED reports oxes occurs 14c.-16c., "but has not survived."
The usage of the plural form oxes can be seen as far as the year 1905 per the latest citation in OED with a plural form of ox.
1905 Hitch my oxes To de plow.
A. V. Culbertson, Banjo Talks 41
Oxford English Dictionary, s.v. “ox, n., sense 1.a”, July 2023. https://doi.org/10.1093/OED/9070656295
OED lists the plural forms below for different periods:
|oexen (Mercian), oxan
|Old English–Middle English
|exon, ocsen, oksen, open (transmission error), oxene, oxis, oxnen, oxon, oxone, oxsen, oxsyn, oxun, oxys
|oxin, oxyn, oxyne
|oxes (now regional)
|oxens (U.S. regional)
Oxford English Dictionary, s.v. “ox, n., Forms”, July 2023. https://doi.org/10.1093/OED/2903238464>
Note that, oxen is mentioned as rare in Old English even, and the plural form oxes survived till modern English period per the citations in OED. There aren't any citations with oxen after the latest citation with a plural form of ox (as oxes) from 1905 in OED. Vocabulary.com has this brief history about -s and -en plural forms:
You may have heard that English is a Germanic language. The -en ending on plurals is something we get from our German roots. In Old English, some nouns were made plural with -s and -es as they are today, but many nouns took -en to become plural.
The s-form plurals became dominant in northern England first, while the en-form hung on in southern England. By the 14th century the s-form became dominant everywhere, but people didn't let go of the en-form completely; as late as the 16th century the plural of eye was eyen and the plural of hose was hosen. Today only a few en-forms survive; the most common are oxen and children.
The above explanation doesn't exactly answer the question though. What happened in history that oxen has become the accepted plural form? Did the southern usage gain traction in time; and if yes, how? Could there be an influential work or writer (from 1900s or earlier) that revived or popularized the usage oxen?
Note: Children and Brethren are other similar exceptions but they don't have the pure plural form with -en and their formation is a bit different than oxen. OED has this note for the plural word children:
In early Middle English, the r-plurals (see Forms 2aγ) are affected by the spread of the (originally weak) plural -en in southern English (see -en suffix3), yielding the double plural children (see Forms 2aδ), which becomes the usual form in southern dialects of Middle English and in modern standard English (compare likewise the development of brethren, plural of brother n.).
Oxford English Dictionary, s.v. “child, n., Etymology”, July 2023. https://doi.org/10.1093/OED/2625064881
The question linked below is related and it has a good answer, but I'm asking something different:
Etymology of certain words ending in "-en"