Originally Posted by Big D
Sephiroth didn't die in the reactor, he entered the Lifestream and eventually wound up at the Northern Cave.
The entity pursued by the party - the one who appears to be Sephiroth - is, in fact, Sephiroth himself - but he's using Jenova's headless body as a means of interacting with the real world. It's much like his resurrection in Advent Children - his mind and spirit occupying a substitute body made of Jenova cells.
This isn't speculation, it's detailed in the Ultimania Omega text. It's also the only theory that's consistent with the events of the game.
The 'Clones', are, as others have said, simply test subjects who are carrying Jenova cells and have wrapped themselves in black cloaks. Because their minds aren't strong enough to resist the cells that have overrun their bodies, they've become virtual slaves to the Reunion instinct, and are completely susceptible to Sephiroth's