These are all correct:
Say hi to your brother for me. (not from me)
Greet your brother for me.
Give him my regards.
But, "Say my hello to him." is not correct.
The most common and least formal is "Say hi to (whomever) for me.
Greet and regards are more formal and less commonly used.
hello used as a greeting when you meet sb, when you answer the telephone or when you want to attract sb’s attention: Hello John, how are you?
Hello, is there anybody there?
Say hello to Liz for me.
They exchanged hellos (= said hello to each other) and forced smiles.
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I agree with tigerpaws that "Say my hello to him" is incorrect, but some non-native speakers may use the phrase. http://tinyurl.com/mf43kz "Pity you wasted all that time. Well, it was nice talking to you, Boake. Say hello to Garvan for me when he comes up." "You mean you're not staying? ...
http://tinyurl.com/ldntj9 Say hello to Fred for me, and to your mother if she remembers me. Good-bye." She had wanted to be free of the other woman, to be alone; for she was still ...
http://tinyurl.com/mp3o53 Say hello to Helen for me, and have a good trip to Guatemala." "Thanks. If you do call, you can say hello to Helen yourself. She's nearly always there. ...
http://tinyurl.com/npxjzt Greet your wife for me, and all the brothers and sisters. God be with you all; remember in the prayer of faith, Your Dear Friend and Brother, HP Scholte. ...
http://tinyurl.com/l4eskr Please greet your parents for me, and tell your sisters I hope they are behaving and not breaking the hearts of too many young men in Uppsala. ...
http://tinyurl.com/njlfjh Give him my regards, and don't remember evil against me. . . ." Myshkin rushed headlong to the street door, where all the party were getting into four ...
http://tinyurl.com/nrpzyk Give him my regards. Give him a bonus." "I'll do that, Herman," I said, and finally closed the door. Sadie had the tea poured in the other room. ...
I have never heard a native speaker say it this way (American English). Also, I have never come across this (say my hello) when reading, either.
"Give my regards to (someone)" is correct and very formal. In my experience this is kind of outdated or old-fashioned.