i've played a TON of OCC's lately and I can now win about 50% of monarch games I play. my most recent strategy has been to play with isabella and go for a hydra diplomacy win.
basically, I found all 3 of the early religions and forgo military while spamming out missionaries of the "one true faith" hoping to bring the whole world in line with my way of thinking
this worked great on prince but monarch has been a little tougher. for this to be a really good strat, I find you need stonehenge to get a GP to build the shrine for your chosen religion first, before going for the pyramids (ie, build stonehenge first, you don't neccessarily need to have the SHRINE built first). you also have to be careful to have enough warriors to use as fodder for barbs since this research path means no metals or archers for a bit. the upside of having the shrine means you will NEVER touch your research slider EVER.
as difficult as keeping decent relations can be in an OCC game, even if diplo is not the victory you want, you need to be able to sow the seeds of war between the ai given your relative smallness. if you get attacked by ANYONE, you should have at least one other ai in your pocket to throw at them.
remember that military cuts both ways for you. you need enough to defend your territory but your territory is small so you'll need less than you would to protect a larger empire. I always try to have at least 4 or 5 of the most current defender on hand and I slowly upgrade the older guys as I can. you;ll also find that if you spam all the buildings you can, you'll eventually get to the point where all you can build is units (you'll have every useful building done).
also remember to avoid building ANYTHING that is not a direct help. you do NOT need a courthouse or (with the exception of stonehenge as mentioned above) any wonder that gives a "per city" bonus.
I find the OCC to be one the most fun variations of civ. enjoy it!