Can we say he was convicted the hung? Is it grammatically right or just an informal sentence? I've seen sentences like 'Sentenced to hang'. But i don't have any idea about this.
to hang has to distinct past tenses: hanged and hung. When we hang a painting, the painting was hung.
When we put a noose around someones head, however, that person is hanged.
When you are convicted, you are convicted of a crime. Because of that conviction, you can be punished, and the declaration of that punishment is a sentence.
So you are not convicted to be hanged, you are indeed sentenced to be hanged.
The complete process could be:
He was convicted of murder and sentenced to hang (or to be hanged).
Which, as @Jim mentions, can be shortened to:
He was convicted and hanged.