Lately, I keep hearing and seeing "embarrassed of..." used instead of "embarrassed by..."

No official research, merely opinion: Perhaps the use of possessive preposition implies that the thing the subject is embarrassed of, is his/her own, rather than some other object embarrassing him/her. For example:

I am embarrassed of my body odour.
I am embarrassed by him pointing out my body odour all the time.

The second sentence is correct, as pointed out. But the first one associates the embarrassing thing with oneself.

I think the correct preposition with "embarrassed" is always "by", not "of", even in the first of Saad Rehman Shah's examples. I agree with Kristina Lopez that this use of "of" probably comes from assuming that "embarrassed" works the same way as "ashamed". It doesn't really work the same way because there is a transitive verb "embarrass" but no transitive verb "ashame". (There is a transitive verb "shame", and I would consider "shamed by" correct and "shamed of" incorrect.)

New Oxford American Dictionary (as bundled natively with macOS) offers nine definitions for "of". The most applicable appears to be the seventh:

preposition

[…]

7. indicating the relationship between a verb and an indirect object.

   • with a verb expressing a mental state: I don't know of anything that would be suitable | they must be persuaded of the severity of the problem.

   • expressing a cause: he died of cancer.

NOAD offers one definition for "embarrass", as a transitive verb (apparently now simplified to the denotation "with object"):

verb [with object]

cause (someone) to feel awkward, self-conscious, or ashamed: she wouldn't embarrass either of them by making a scene.

• (be embarrassed) be caused financial difficulties: he would be embarrassed by an inheritance tax.

It would seem then that the "embarrassed of" usage would be a mixing of a verb whose usage is exclusively transitive (expecting a direct object), with a preposition whose most relevant usage is expected to be intransitive (for an indirect object).

Thus, it seems to be nonstandard, but I personally feel the meaning it conveys is quite understandable.

The use of embarrassed of has been bothering me for quite a while. It just sounds very awkward - and incorrect, although I have no rules of grammar to back me up. I grew up hearing and saying embarrassed by but now I never hear that anymore.

Adele sings a song in which she uses the phrase we were sad of getting older and this strikes me as just as awkward.