I wash me on hair
"me" is the direct object (i.e. accusative) for the transitive verb "wash sth.",
and "on hair" is a prepositional complement and not the actual object of the washing (grammarwise)
PS. This is confusing for German speakers, who would say something like:
"I wash to me (dative) the hairs (accusative)" - so it's the hair that gets washed directly.
[Ich wasche mir die Haare -> Rumänisch: Ich wasche mich über Haar]
Romanian has also the dative variant "Eu îmi spăl părul / mâinile/ fața picioarele " but for some reason the most common used is the "pe" variant "Eu mă spăl pe păr/ mâini/ față/ picioare"
Eu mă spăl pe cap (lit. "I wash me on head"; "Ich wasche mich über Kopf") is also common, with the same meaning and pattern.
Yes, and pe is probably not even actually interpreted by Romanians (pe = Lat. per or super), but the dative mir to accusative mă thing will haunt me for a while. It is probably easier for English natives who need to learn it by heart anyway as they do not "feel" the cases of declension.
In English a reflexive verb is not needed but you need the possessive adjective (my).
In German the possessive adjective becomes a pronoun akkusative if you don't say which part of your body or dativ if you say which part
Ich wasche mich. Ich wasche mir die Haare.
In Romanian the possessive adjective becomes a pronoun and we have seen that we write "pe" before direct objects
Eu mă spăl pe pâr.
In Spanish the same thing but without "pe". We use an article. The possessive pronoun is not needed because it is supposed that you wash your own hair if you wash somebody's hair the reflexive pronoun is not needed
(Yo) Me lavo el pelo.