This “Barney & Clyde” strip was submitted by Usual John:
I think the gag is that the strip itself does not have (and does not need) a gag, but I’m sure there are other possible explanations.
I went hunting to see if there were any other worthwhile April Fools’ strips, but was sorely disappointed. Almost all of the “standard” setups simply showed one character playing a typically lame practical joke on someone else. The best strips were those few that elevated the humor with some sort of “meta” component. Here are a few examples:
(I especially liked this “Thatababy” strip because this year, my daughter decided to rearrange the silverware drawer as an April Fools’ joke. Unfortunately, it didn’t work, because we all just assumed that she had forgotten the usual arrangement.)
The last two examples are from the great Comic Strip Switcheroo (1-Apr-1997):
P.S. Feel free to embed your own favorite April Fools’ comics in the comments!