Sit down, take a deep breath and relax.
Always start with the basics.
With the car on level ground, open the hood and find the engine oil dipstick (should be near the front of the engine bay. Check your Owner's Manual if there's any doubt). Pull it out, wipe it off, reinsert it and pull it out again to check the oil level. It should be between the two markers.
Next, locate the automatic transmission dipstick toward the rear of the engine bay. (correction per BlackMercedes:
"The W202 C-Class and W203 C-Class C230 models do not have a dipstick for the tranny fluid as they use the 722.6 five speed automatic. You'll have to buy the dipstick from the dealer.
Also, on the 722.6, the tranny fluid level must be set while the fluid is at 80C. Use ONLY the MB synthetic fluid, or you'll probably wreck the tranny.
I don't recall the tranny having a drain plug.")
If you over filled the crankcase it will be immediately evident. If you drained the transmission, nothing will register on the stick.
Start by refilling the trans with MB Synthetic Trans Fluid.
(correction by sixto:
If you don't know how much transmission fluid you drained, fill in half quart increments until you get to 10mm below the lower tick mark on the dipstick. That should be enough fluid to get the car running (once the engine oil issue is resolved). From this point, fill only with the engine running and the transmission fluid at operating temperature. That means drive the car. The transmission doesn't get to operating temperature by idling the engine.)
Be scrupulously clean and don't let any foreign material enter the trans. Even lint from a cloth used to wipe off the dipstick can cause a problem. Use a lint-free cloth or a good paper towel and check it before you put the dipstick back in. If you really did drain the trans (the fluid would be red), you'll have to pour in as much as you drained. If possible, fill until it just registers on the dipstick. Later on, when the engine oil is taken care of you can drive the car for 10 min. or so and then recheck the trans fluid level and top it off.
If the engine oil reads overfull on the dipstick get the car up on ramps (running the engine the least amount possible), get under the front of the car, remove the plastic shield and locate the engine oil drain plug. It should be located on the side of the aluminum sump toward the front of the engine. Get a couple of drain pans ( you could have upwards of 10 quarts in there), unscrew the drain plug and see how much comes out. Engine oil, depending on how long it's been in the engine, can appear dark amber (newer) to almost black (been in there a while) or some shade in between. If you're draining transmision fluid, it will be noticeably reddish in color and doesn't really change much with age.
Once you've determined that it's engine oil you're draining, confirm that there's approximately twice as much as there should be, replace the drain plug, torquing it the proper amount (good and snug, not real tight) and refill the crankcase with the proper type and amount of oil. Start the engine (it may still smoke for a while), let it idle for a minute or so, turn it off and recheck the oil level. Also check for any oil leaks at the drain plug or elswhere. If any develop in the near future it's possible that you blew out a seal or gasket from too much oil causing too much crankcase pressure. If that's the case go see a good service tech and have it checked out.
In the future you might want to invest in one of the suction-type oil sump evacuators like the Topsider
or the Mity-VAc
which use a long tube inserted in the oil dipstick tube to suck the oil out. It eliminates the problem of undoing the wrong drain plug and saves you having to crawl under the car. They cost from $45 to $55USD.
Hope this helps,