Two questions:
1) How's the damage?
2) How many levels of monk?
Depends on the exact build.
Assuming I'm not using a variant Monk base class with relaxed multiclassing rules- WotC's published quite a few- for most of them, it's predominantly Monk with Monk-friendly PrCls, like Kensai, Shiba Protector or Shou Disciple. Occasionally, I'd start with 2 levels of Ftr or PsyWar for feats before going into Monk & Monk PrCls for the duration.
As for damage, with the last 2 polearm Monks I played, the githzerai monk was matching the party's 3rd lvl Brb (sans Rage) while not being hit; the Monk/Kensai with a Greatspear did the bulk of the melée damage to a pair of Green Dragons at an ENWorld Gameday. The poor reptiles kept triggering AoOs, and my +4 from Deft Opportunist made sure I hit often, and when they were out of range, I harried them with javelins to supplement the caster's attacks.
Discounting the Dex monk's advantage on initiative, without burning feats for the polearm build, the melee DPR is lower than for a Str build monk. But even so, it does nearly as much damage over the first 5 rounds of combat due to increased probability of doing decent damage with a crossbow- a weapon for which there is no Str bonus in it's use- at range, and will have, on average, more HP due to being missed a bit more often.