In order to create smoke, you need to raise the wood chips to the temperature at which primary (but not secondary) combustion occurs. A very good explanation of how wood burns is here.
Primary combustion happens when the wood is hot enough that gases are released, but not hot enough that all of the contents of those gases completely combust. This material that is combustible (just at a higher temperature) and is released from the wood is smoke, and that's what you want to get released from the wood chips in order to smoke something.
Wood doesn't begin this process until about 540 degrees fahrenheit (282 Celsius) so unless you heat the wood to this temperature you're going to get basically no smoke at all. This won't happen in a 200 degree oven - actually, it would probably be hard for it to happen in an oven at all - and even if you did have your oven hot enough, you'd likely end up overcooking your food long before it absorbed enough smoke.
So since the wood chips need to be quite hot, and the temperature around the food needs to be significantly cooler, in order to smoke something you really need a way to create this large temperature difference while making the smoke travel from the hot wood chips to the cool food. This is why most smokers have some sort of separate burning chamber that produces smoke but doesn't directly heat the meat and thus allows the cooler temperature. This is also why you put the wood chips directly on or over the heat source when smoking on a grill.
Joe mentions that smoking can be done on the stovetop, and this makes sense since you could place the wood chips directly on the bottom of a pan and thus heat them very hot, but put the food higher up (maybe even let some cool air in) in order to keep it at a much lower temperature.
Any other way that you could achieve this high temperature differential could be used to smoke food - for example, you could set up a separate smoking box with a duct (you might need a fan depending on your setup) running into your oven - maybe you could heat this on the stove, or have it outside. If you had an exposed element at the bottom of an electric oven, you might be able to set a little box of woodchips on or right next to that to get it hot enough (you may destroy the element though...). If it's a gas stove, perhaps there's a way you could put the chips directly on or under the flame in order to get the high temperature. If you turn your oven on to around the temperature you would smoke at, you could check the surface temperature of your oven in various places with a IR thermometer and see if there were any extra hot places. These might be good places to put your wood chips. And as an aside, you'll probably want a fire extinguisher handy for most of these just in case.
On soaking the wood chips - The main reason to soak woodchips before smoking is to avoid full combustion. To produce smoke, wood needs to combust inefficiently, and one way to do this is to make sure its temperature stays below ~1100 degrees fahrenheit. The water helps with this because it takes a huge amount of energy to boil off water which must be done before the temperature can get above 212F (the water towards the inside of the chips boils and cools the outside of the chips as they combust - so you'll still have water in the woodchip while the outside is smoking). In order to make it easier to achieve smoke faster, you might want to try not soaking the chips so they get to primary combustion faster, but then limit their combustion in other ways to ensure that they don't produce enough heat through their own combustion to achieve secondary combustion (no smoke). You could do this by regularly spraying the chips with water after they begin smoking, or by limiting the supply of oxygen to the woodchips - the latter might be achievable if you rig up something like a smoking box on the stove with a duct into the oven with vents you can close.
One more note, you're going to end up with a lot of smoke inside, and you really don't want to be breathing this (carbon monoxide, among other things), so please make sure you have a lot of ventilation going on when you try this. And maybe a carbon monoxide detector nearby to be safe.
Edit - Wikipedia mentions in the Wood Smoke section of the Smoking page that the best smoke is produced by wood between 570 and 750 degrees fahrenheit.