i just changed my radiator as well about a week ago in my 96 accord... you may have some smoking because of ATF that had dripped out, i had some in mine. once it burns away after letting the car sit and run for a little bit it should go away... if not i would deffinately look at both of the small hard lines that connect to the bottom of the radiator, the leak may be from: bad connection from the hoses to the hard lines or because of moving, tugging and pulling of the radiator you may have rust (I.E. on the relay hard line that runs from the passenger side to the driver side, that was a bad line for me that needed replaced) that could have broken and is causing the leak.

Im not going to lie though, if you know that the smell is burning oil then i don't know what that could be caused from. (I'm just a backyard mechanic, i don't know how to fix a problem until one comes up and i havnt had something like that happen yet *knock on wood)