In general, your initial strategy should be to kill low level monsters, seeking out anything which can mitigate your initial attack penalty; level 1 meat men will do 0 damage to you. Any shop items which reduce damage are of special interest to monks. A platemail or mage plate will bring your resistance up to an insane 70%.
After the first few levels, monks should seek out higher level enemies with low damage and high health. Because of monks' faster healing and high armor, they can often refill health via exploring without the monsters having enough time to do the same.
Glyphs of special interest to Monks are:
Race and Deity Choices
Playing as a human to compensate for the hand to hand penalty is typically the best choice. Attack damage bonuses have a higher proportional effect for monks due to the lower initial damage.
Monks are incredibly effective fighters once their attack penalty is canceled out, but the value of their health can make sacrificing HALPMEH and LEMMISI too painful to make Taurog a strong choice. The Pactmaker is an excellent choice for any class, Monks included. Going after Tikki Tooki is practically a deathwish that will end up stripping you of your resistances, as is Jehora Jeheyu. Dracul is also surprisingly useful in non-Crypt challenge levels, as the combination of Bloodshield and Bloodhunger turns you into an even bigger defensive powerhouse.
Poison Monk Strategy
Because of the monk's resistance, it has a heightened ability to survive first attacks. This means you can, upon finding APHEELSIK, wear down higher level monsters with up to twice as much attack as other characters! Using your spare mana for BURNDAYRAZ (or BYSSEPS or CYDSTEPP) plus taking advantage of your double HP regeneration you can level catapult in greater comfort than other classes.
Due to the anti-melee properties of all monsters here, this is a very difficult challenge for the monk. You'll require a good combination of skills and gods. Once such combination is HALPMEH and Glowing Guardian, possibly coupled with BYSSEPS or CYDSTEPP if you can find them. HALPMEH will quickly earn you piety as you take out Gorgons up to 3 (!!) levels higher than yourself. You'll be able to gain Absolution around level 7, which will enable you to take out Jormungandr fairly easily. Use HALPMEH to undo his poison, and level-up midfight if you can. It's easy enough to get a few piety points from Glowing Guardian to offset having to kill lower-level monsters for that level-up, in fact if you get the Guardian early enough, you might even be eligible for a healing which will help greatly against either boss.
Naturally, buying Immunity from Death Gaze will make this dungeon significantly easier. Don't waste your money on Immunity from Poison if you can find HALPMEH. If you can't find it, it's not likely that you can win the level anyway.
Also, consider switching Human for Dwarf, as the extra health will come in handy.
Another viable strategy is to pick up BURNDAYRAZ as soon as possible and use it to soften up higher-level enemies. If you pick Human and focus on increasing your attack damage (eg. Fine Sword), you can usually take out Gorgons 1-2 levels above. Avoid Nagas and to some extent, Serpents unless taking them out levels you up. The general advice to pick Dracul for Bloodshield and Bloodhunger works well here. If you manage to find APHEELSIK, the Poison Monk strategy would also go well with this.
Total key here is Taurog. Not only he will boost your low damage, he will also remove Tormented One's insane defenses. Begin to worship early, convert all your glyphs and accumulate enough piety to gain Fury and Penetration boon. Due to your high defense and increased regen you can explore during battles to outlast any given foe around 2 levels higher than you - experiment a little and you will see. Level up to 7 lvl, and begin to smack the Tormented One. He will succumb quickly to your attacks. Same goes for Frank, but you can also use potions here to speed up the process.
You can also use HALPMEH for benefit - kick enemy, explore 1-2 tiles and heal, then kick again. Monk is about endurance and outlasting foes, after all. If you rely on HALPMEH - consider Glowing Guardian as option to hit enemy a little bit more times.
If you manage your health, mana and xp cleverly you'll have both bosses defeated before coming near level 9. You can even kill the Tormented One without his defenses breached, but in this case you're going to need HALPMEH and Soul Orb to protect you from mana burn.
After a few levels you can easily defeat Dragonspawns 2-3 levels above you with fast regeneration. Having HALPMEH and/or LEMMISI will make things even easier. If neither of those is found, you can use fireballs to accumulate damage.
Once you have reached level 3-4, the combination of high armor and fast regeneration should make it fairly easy to kill higher level animated armors. Attack the highest level animated armor you can that cannot kill you in one hit. The assistance of BURNDAYRAZ will make this more efficient, though HALPMEH or LEMMISI are a reasonable substitutes.
Super Meat Man is rather easy to defeat with monk, especially if you have bought the tower shield or platemail. Try to be at level 8 or higher before fighting the bosses. It should be possible to heal (via some mixture of HALPMEH, LEMMISI, and exploring) faster than Super Meat man can damage you.
The Iron Man doesn't have much health, so killing him should be fairly easy. You should still have most or all of your potions at this point, but you may want to time this fight to enable you to level up in the middle of it to assist further.