I have had that similar experience only with automotive paint being the overspray. I **** you not man this is what you should do (assuming you have a corded or cordless drill):
1) Purchase a POWERBALL for paint $20. (autoparts store will know what it is if you don't) and some non-abrasive paint cleaner( I use meguires step 1).
2) Wash car thoroughly by hand to remove the dust and other debris that could scratch your car while you powerball it.
3) Go over the entire car with powerball. You can slide your fingers across paint while you do that to make sure the overspray has been removed.
4) Follow up with paint polish ( I use meguires step 2) and I dont use the powerball on this process because I let the chemicals do the work to prep the paint for the wax.
5) Wax that beautiful example of german engineering. ( I use mequires fx)
6) Admire that paint job because I guarantee it will have never looked so good or felt so slippery.

 

Clay bar will work just fine. Thats almost exactly what clay bar was made for. For the spots it doesn't work on you should be able to get it off w/ stuff others have mentioned. I have a product called Eradicator made by Car Brite that takes just about anything off paint w/o hurting it. I think its basically the same thing as mineral spirits but not sure. I tried to find out but it doesn't say whats in it but either way it says its made to remove tar from paint and can also be used as a spot remover inside the car. It works great outside but I have had better luck w/ Windex on the inside haha. Who knew that Windex could remove a coffee stain so well! Anyways I would go get yourself a gallon of Eradicator. Your local parts store should have it and you can put it in a spray bottle to use it. Just thoroughly wash and wax the car when your done because it takes all the wax off your car.

 

Seconded - many people have said that a claybar can remove it. If it doesn't, try a mild rubbing compound or a high-speed buffer (make sure the person running the buffer knows what they're doing or they'll remove the OEM paint along with the overspray).

 

DO NOT USE ANY ABRASIVE COMPOUND! NONE! DON'T! You've got overspray from 200 feet away. The **** was practically dry by the time it hit your car.
I had a more serious issue regarding overspray than you do currently.

Powerball vs Claybar

Powerball you can do your entire car in a matter of hours, you don't any experience and it wont burn through the paint. Itworks as well as a professional buffer. Clay bar is good and will do the job but I only use it for spot treatments (You know how big a pain it is just to wax the car. Get a claybar to do this job and unless you are the most **** sob out there you will half-*** it and get half *** results). $20 on a powerball is the best $20 I've ever spent on a detailing product and I have literally spent thousands on my cars. In my younger days I managed the reconditioning department for an automotive dealer a larger one not a small lot, so I've done it all as far as reconditioning goes. Don't get me wrong claybar is great product but I GUARANTEE the power ball (for paint) Is going to give you the best results hands down! For the record I have a $350 napa buffer/polisher that is now a dust collector($250+ship if you want it). I prefer the powerball for paint. Think about it your average drill driver will spin that powerball at 1750 rpms how fast would you have to move to compete against that with your hand and a claybar.

 

^ Finishing compound will work like powerball and also improve the look of your paint

 

i guess i'll try some of these and see how it goes!

 

for the best and complete results- wash your car with dawn dish soap, dont scrub too hard because you have crap in your paint... it will scratch. the dawn will take off everything, all the wax. some say follow with a good normal car wash soap.. i dont know why..
clay bar, meguiars kit costs $15... theres another kit on the shelf that is the same, comes with two bars.. i got that one. this will take the overspray off.. you hope.
IF you want to restore your cars clear coat, this is a great time to use a buffing compound, use meguiars. this is recommended for professionals or experienced do-it yourselfers so if your asking you probably arent experienced enough to do this.
use a meguiars professional series polishing compound.. use the meguiars or some other brand that does'nt use silica or silicone (pretty much sand) but rather clay because it breaks down into fine particles after doing its job and wont scratch.. this is especially important if your car is black. i wouldnt use the all in ones or two in one buffing polishing waxing blah compound.. that stuff is crap.
glaze! glaze is important, trust me. youll never see your car shine so much.. and its really fun surprisingly! it will restore all the lost oils into your cars primarily organic clear coat. trust me, do it. i use meguiars #7 show car glaze.
wax. use a paste wax. i use meguiars NXT because it has an RX7 on it.. and coming from an RX7 owner, it cant be bad if it has a Mazda on it!
if your ****, use a spray wax on top of that and every time you wash it.
when you wash it, dont use dawn because it will take off all that hard work down to the clear coat. find a wash that just.. washes it.

dont take my word for it, i am no seasoned professional. read tutorials. educate yourself!
i can promise you, youll AT LEAST want to dawn, clay bar, polish, glaze, and wax for a respectably restored paint job.

 

^ They say to follow with a good car wash soap because Dawn has silicone in it. I don't know about regular work but silicone+body work=BAD!

 

Dishsoap also causes your black vinyl trim to oxydize and weep. I wouldn't make a habit out of using it unless your into greying black trim and damaging your weatherstriping. To use an old addage "there's more than one way to skin a cat" as well there is more than one way to remove overspray from your car. Some ways are going to take much much longer than others. I did recondition vehicles professionally, have ordered products from a variety of vendors and know there are alot of products out there that will get you the results you want. I only mention the powerball (for paint) because it works amazingly well and it will take a fraction of the time versus other methods. Like I said before I assume that a good portion if not all of your car is covered in this overspray so I figured I would suggest a method I have used that is inexpensive and relatively quick. Like rellimmot I also prefer the meguiars products. Claybar=good for spot treatments and a panel here and there but I think you will find that it takes a ridiculously long time to scrub overspray off your entire car with a claybar. Time is important to me, not to some, but to me.

 

do full detailing job with clay, buff, polish, wax, etc. it'll be all gone. next time bring a tarp if you're gonna park close lol