As a ukulele player myself, I recommend it as the solution to many problems, both great and small--and it is perfect to use in this situation--it will have a much better effect on the audience than a piano, and even a minimum playing effort will please the audience--

With the uke, the strumming is really the most important thing, so find the simplest chord to each song--

For the "minimum", just brush your thumb down over the strings(an arpeggio, if you really need a name for it) once for each measure or for each new chord, whichever comes first--make sure you do it confidently and loudly, and remember that Will Rogers said(approximately,"When you play the ukulele, it sounds like you're just fooling around with it"--

If you feel inspired to do more, try using a basic strum, performed as Mark described above, with the index finger, the pattern is
"Down DownUp DownUp DownUp", and sound like "Boom walla walla walla"--

Find some recordings of George Formby to get a feel for it--Cliff Edwards(Ukulele Ike) was one of the best, and worth listening to, but
Formby was a much more basic sort of player--

As for who played them, nearly every one--in their time(the were introduced to the world at large at the San Francisco Exposition in 1915) they were a much favored instrument to accompany informal singing--

From 20's on, they were popular with variety and stage performers, particularly for humorous and novelty tunes, and they were often used by college men to serenade--for a group of adult women in 1944, particularly those who had enjoyed singing together since youth, the ukulele could be very evocative of times gone by--

For a great moment in Ukulele Cinema, check out the 1952 film "Belles on Their Toes"(sequel to "Cheaper By the Dozen") Hoagy Carmichael plays and sings "The Japanese Sandman" while strolling at the beach--