stink bomb; weasel's defensive odor
Literal meaning: the foul smell released from a weasel's anal sacs when frightened. Also used for a stink bomb or similar prank item.
He brought a stink bomb into the classroom as a prank.
When attacked by an enemy, a weasel releases a foul odor from its anal sacs.
last-ditch tactic; final desperate measure
Idiomatic use: a final, often underhanded or desperate, tactic employed when all else has failed. Conveys a sense of a last resort that may be unpleasant or sneaky.
With negotiations about to break down, he proposed a price cut as a last-ditch tactic.
The candidate, facing defeat in the election, resorted to a desperate final measure.
最後の手段 is a neutral 'last resort', whereas 最後屁 carries a nuance of a sneaky or foul-smelling last-ditch effort.
Literally 'last fart', from 最後 (last) and 屁 (fart). The literal sense refers to the foul odor emitted by a weasel when threatened. The idiomatic sense extends this to a final, desperate, and often underhanded tactic.