I'm not sure Origen believed in reincarnation rather that the soul pre-existed the body. Origen did have some funny views though, which is why he was posthumously anathematised by the Church.
I don't think reincarnation is held by anyone except on the fringes, new agers and semi-buddhists. It's not anywhere in the scriptures.
I'd be interested to hear the Christian take on these notorious scriptures then:
"Behold, I will send you Eli'jah the prophet before the great and terrible day of the LORD comes.
And he will turn the hearts of fathers to their children and the hearts of children to their fathers, lest I come and smite the land with a curse"
Malachi 4: 5,6
" And the disciples asked him, "Then why do the scribes say that first Eli'jah must come?" He replied, "Eli'jah does come, and he is to restore all things;
but I tell you that Eli'jah has already come, and they did not know him, but did to him whatever they pleased. So also the Son of man will suffer at their hands."
Then the disciples understood that he was speaking to them of John the Baptist."
Matt 17: 10-13
" And they asked him, "What then? Are you Elijah?" He said, "I am not." "Are you the prophet?" And he answered, "No."
"They asked him, "Then why are you baptizing, if you are neither the Christ, nor Elijah, nor the prophet?"
John 1: 21 &25
(The last one, of course, being a contradiction of what Jesus is supposed to have said in the previous quote.)