while i most of the times win at deity, after a couple of hours i left the game and restarted at a lower level...

I think you must get bombards by around 1700 or as soon as possible, or else you can get blown away by a massive enemy ship bombardment. I think if you stuff 3 or 4 bombards into every coastal city you can hold them off long enough for peace. I haven't actually tried this.

I think you have to stay away from building cities on enemy-dominated lands, because they can overrun you by land no matter what you do.

Eventually I think you can get an ally and demand techs, then I guess you go out and try to take over the internet or the lead ai capital with a bunch of howitzers, I never played that far. Maybe there are more surprises. Note you can demand a tech from even red-face ai's once it seems (suggestion: gunpowder). Also you can build a city and disband it to build a garrison of militias anywhere (which disappear with the next defensive troop advance). Don't know if that's useful.

It seems strange the computer likes to research future tech 10 instead of useful advances, or building the space embryo (fortunately!).

I'll have to venture into the future realms one of these games. I've been busy so far just making sure I can always survive through the 1800s :-)

Basically I have only found one way to do well at diety level, a way which tends to exploit the things the ai is not good at (ie battle, navy, slaving). Generally I play with 16 civs on a regular map (or one size larger) with ravaging hordes and settings that provide a fair amount of ocean space with two or three continental masses. Currently I have the disseminate trigger disabled since there is some question concerning it and since the only time I played with it basically it eliminated technology races. ( I think perhaps that is due to the number of civs I'm using)

So far I have found only one way to make up for the
population difference at the beginning of the game and that is through extensive use of slavers. After getting a handful of cities going I usually create a stack of 3-4 units including a single slaver and then begin growing my population by picking up stray ai units and barbs. (Its important not to irritate all your neighbors since at this point in the game they tend to have more numerous and stronger units) This allows for population growth while additional settlers are built. In addition, growing population through slavery allows workers/slaves to be placed on terrain favoring production/gold instead of food. The increased production makes possible the build up of a small army (which also includes a slaver) as well as additional slaving bands while the gold helps keep one in the game in the tech race.

After a fair number of cities are built and a small army ready I typically pick out the most belligerent neighbor and prepare to attack. Sometimes its useful to pick a civ that has built a particular wonder that you like. (By the way at this time I'm typically well in last place on the power graph) Thus begins the conquest which basically has to continue for the entire game. I have never had success trying to outgrow/ outbuild the ai players without major slaving and conquest.

I just began a new game last night and its going fairly typically. After about 130 turns (i.e. somewhere around 1200) I have conquered one neighboring civ and have reached a point in the power graph where I am number eight. I haven't had a status update but I expect that I have nearly as many cities as the leading civs and of course because of the slaving I have the two largest cities (nice because with the big production they can produce defensive units in one turn to occupy newly captured cities). I have three moderate sized armies (6 units). According to diplomacy there are a couple of civs which are strong, maybe seven average and the rest weak or very weak compared to mine. I have an embassy with the number four civ and can see that they have a tech advantage of 5 techs (I didn't get out of monarchy early enough).

The biggest challenge at this point is making up the techs. A few weeks back I played a game where I finally caught up with number one on the power graph in about 1800-2000 (a typical time period to make it to the top) and found that even though I had more pop,cities, gold etc. that they had maybe 20 more techs. It took quite a bit of larceny and battling to make that up and it tends to leave one open to special attacks and small attacks by considerably better units (sometimes dropped from space). The best way to avoid having this happen is of course to go and attack the more powerful civs at an earlier time in the game, thereby providing yourself with new knowledge and in general limiting their ability to develop new stuff. Just don't wait too long because once the ai develops better units, although they aren't too smart at attacking, the better defensive units can make it nearly impossible to take their cities.

I know that this is conventional wisdom, but I hope it is helpful. I would also be interested in whether anyone has succeeded using a strategy that didn't include major conquest, like outgrowing/learning the ai on a giant map.