In regard to 'Smoking or Non Smoking', it is Hudson making a joke. Not really sarcastic.
He has people locations on the screen in front of him (like someone would have if they were taking a reservation for an aeroplane seat), he is just playing, being silly, by pretending to be making seating arrangements.
'Stop your grinnin' and drop your linen'
loosely re-worded could be:
'Stop smile(ing) and drop (remove, take off) your clothing'.
I don't know where this line could have originated, however, it would be spoken by a man to a woman before sex.
In the context of the film, it makes no sense. He could have said 'Stop what you are doing. I have a result from my search on this computer. Now we are ready for the next step', Hudson is just trying to use a clever line and be funny. Tough boys always talk about sex etc.
Cheers.