yes, however, as a landlord/RE agent, i'm highly skeptical of one nighters. i've had too many experiences with batchelor parties, crap games, escort women, porn video producers, etc.
might take you a while to find what you're looking for
yes. It must be a vacation rental which can have nightly, weekly, and monthly rates. Many require a three night minimum however. Aside from craigslist.org, one can find such homes for rent by their owners (not agencies) on the internet sites vrbo.com and airbnb.com or homeaway.com vacationrentals.com chbo.com crbo.com westside rentals.com etc. The rates for one night rental of a house could begin as low as $90 (depending on location and the house). They could soar up to $10,000.00 per night for a house.
We don't usually see listings of that nature on the MLS. As mentioned below in the comments from my colleagues you can try those websites, craigslist or by googleing vacation rentals and see what comes up.