It's Ok to end a sentence with of but most of those sentences are all awkward as they are really about possessives and not verbs followed by OF and a noun. We tend to find less awkward ways to avoid of which,by which or whose, etc.
For example: That's not someone I've heard of.
[to hear of something or someone]. There, the of would be used.
1) He's somebody I like the personality of.
That would be generally phrased something like this: He's one person with a personality I like. [thereby avoiding whose].
When one likes (hate, dislike, love) something or someone, that is a direct object. There is no of. Also, English likes possessives: I like that man's personality. or: He has a personality I like. That's man's personality is something I really dislike.
That said, more sophisticated speakers often do say things like:
He's someone whose personality I like.
These speakers do not necessarily avoid of which, whose, etc. all the time as colloquial speakers would.
That sentence makes sense if discussing personalities. A more natural rendition of it would be: People like that have personalities I like.
2) It's a song I hate the lyrics of. [same as above, there is no need for of]. That's a song with lyrics I hate. [with, as in 1), avoids of which or whose].
3) She can't date someone she doesn't like the appearance of. [this one works better because there is: like or not like **the appearance of a person though we generally say: a person's appearance]
Generally speaking, it is the verb followed by OF + a noun that will trigger a non-awkward final of:
- There really was no matter to speak of. [to speak of a matter as in to discuss]
In most other cases, look at your implied possessive: the personality of the man, [the man's personality]; the lyrics of the song, [the song's lyrics]; the appearance of a person (a person's appearance); pictures of the girl, the girl's pictures.
- She can't date guys with personalities she dislikes.
- They dislike songs with lyrics like that or those types of song lyrics.
Mostly, in the numbered sentences, there is no need for a final of with these verbs. Native speakers avoid those hidden possessives by using a possessive or by using a construction with "with" or some other construction in construction with like, dislike, etc. unless it's a preposition + noun.
We have nothing to talk about. [talk about something]