Does Hunker Down stop the effects of siren Siren's Song, or any opponents "move a unit" effect

Yes — a unit under Hunker Down can't be moved by Siren's Song or any other opponent's move effect. Hunker Down's "It can't move this turn" is an absolute restriction, and move instructions that can't be followed are negated when the spell resolves, not merely delayed (Rule 54 "Can't beats Can"; Rule 359.3.e.14.b uses the same reasoning with Vilemaw's Lair's "units can't move from here to base").

The opponent can still cast Siren's Song at it — "moved this turn" is still true, so it's a legal target and the spell doesn't fizzle on targeting — it just resolves and the move does nothing. Hunker Down also being [Reaction] means you can play it in response to the Siren's Song itself and it will resolve first.

Two caveats worth knowing: this blocks every kind of move (Standard Move, Showstopper, Ride the Wind, Siren's Song), since the restriction doesn't care who is doing the moving — but it does not stop a Recall, because a Recall isn't a Move (Rule 448.1). Also, nothing else about the unit is affected: it's still a legal target for kill/damage effects, and it's already readied by Hunker Down.