I found a funny article on Wikipedia listing unusual units of measurement. Below are some that caught my eye:
The beard-second is a unit of length inspired by the light-year, but used for extremely short distances such as those in nuclear physics. The beard-second is defined as the length an average beard grows in one second. Kemp Bennet Kolb defines the distance as exactly 100 Ångströms, (i.e. 10 nanometers) while Nordling and Österman’s Physics Handbook has it half the size at 5 nanometers
A measure of distance equal to about 7⁄8 of a mile (1.4 km), defined as the closest distance at which sheep remain picturesque. The Sheppey is the creation of Douglas Adams and John Lloyd, included in The Meaning of Liff, their dictionary of putative meanings for words that are actually just place names. It is named after the Isle of Sheppey in the UK.
The smoot is a unit of length, defined as the height of Oliver R. Smoot — who, fittingly, was later the president of the 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 includes the smoot as a unit of measurement.
This facetious engineering unit is defined as 250 watts—about a third of a horsepower.
The Friedman is approximately six months, specifically six months in the future, and named after columnist Thomas Friedman who repeatedly used the span in reference to when a determination of Iraq’s future could be surmised
The Wheaton is a measurement of Twitter followers relative to celebrity Wil Wheaton. The measurement was standardized when Wil Wheaton achieved half a million Twitter followers, with the effect that Wil Wheaton now has 3.4 Wheatons himself. As few Twitter users have millions of followers, the milliwheaton (500 followers) is more commonly used.