Wikipedia has a list of Humorous units of measurement, in addition to their List of unusual units of measurement. The humorous units are better, although the two lists are not mutually exclusive. the humorous units all have funny stories behind them, but some stand out because they are actually used.
One mickey is the smallest resolvable unit of distance by a given computer mouse pointing device. It is named after Walt Disney's Mickey Mouse cartoon character. Mouse motion is reported in horizontal and vertical mickeys. Device sensitivity is usually specified in mickeys per inch. Typical resolution is 500 mickeys per inch (16 mickeys per mm), but resolutions up to 16,000 mickeys per inch are available.
The Smoot is a unit of length, defined as the height in 1958 of Oliver R. Smoot, who later became the Chairman of the American National Standards Institute (ANSI), and then the president of the International Organization for Standardization (ISO). The unit is used to measure the length of the Harvard Bridge. Canonically, and originally, in 1958 when Smoot was a Lambda Chi Alpha pledge at MIT (class of 1962), the bridge was measured to be 364.4 Smoots, plus or minus one ear, using Mr. Smoot himself as a ruler. At the time, Smoot was 5 feet, 7 inches, or 170 cm, tall. Google Earth and Google Calculator include the smoot as a unit of measurement.
The Cambridge (Massachusetts) police department adopted the convention of using Smoots to measure the locations of accidents and incidents on the bridge. When the original markings were removed or covered over during bridge maintenance, the police had to request that someone reapply the Smoot scale markings. During a major bridge rebuild, the concrete sidewalk was permanently divided into segments one Smoot in length, as opposed to the regular division of six feet.
A Wiffle, also referred to as a WAM for Wiffle (ball) Assisted Measurement, is equal to a sphere 89 millimeters (3.5 inches) in diameter – the size of a Wiffle ball, a perforated, light-weight plastic ball frequently used by marine biologists as a size reference in photos to measure corals and other objects. The spherical shape makes it omnidirectional and perfect for taking a speedy measurement, and the open design also allows it to avoid being crushed by water pressure. Wiffle balls are a much cheaper alternative to using two reference lasers, which often pass straight through gaps in thin corals.
Barn, outhouse, shed (area)
A barn is a serious unit of area used by nuclear physicists to quantify the scattering or absorption cross-section of very small particles, such as atomic nuclei. It is one of the very few units which are accepted to be used with SI units, and one of the most recent units to have been established (cf. the knot and the bar, other non-SI units acceptable in limited circumstances). One barn is equal to 1.0×10−28 m2. The name derives from the folk expression "Couldn't hit the broad side of a barn", used by particle accelerator physicists to refer to the difficulty of achieving a collision between particles. The outhouse (1.0×10−6 barns) and shed (1.0×10−24 barns) are derived by analogy.
A Pirate-ninja is defined as one kilowatt-hour (3.6 MJ) per Martian day, or sol. Andy Weir, author of The Martian, revealed in a 2015 interview with Adam Savage that the Curiosity rover team at the Jet Propulsion Laboratory references milli-pirate-ninjas in their meetings.
In nuclear physics, a shake is 10 nanoseconds, the approximate time for a generation within a nuclear chain reaction. The term comes from the expression "two shakes of a lamb's tail", meaning quickly.
The Garn is a unit used by NASA to measure nausea and travel sickness caused by space adaptation syndrome. It is named after astronaut Jake Garn, who was frequently sick during tests and on orbit. A score of one Garn means the sufferer is completely incapacitated.