There is indeed something known as long vs. short syllables. It is a borrowing from Latin and Greek poetry. Any syllable with a long vowel, any syllable with a dipthong, any syllable with a short vowel followed by more than one consonant, is a "long syllable" - as in, it literally takes longer to pronounce. These are also known as "heavy syllables" as opposed to "light syllables." The Latin form terms were "longum" and "brevis."
For instance, "am" is a short syllable. "Arm" is a long one. "Aim" is a long syllable. And the first syllable of "Amy" is a long syllable. This is not the same thing as stressed vs. unstressed syllables though I think it is natural for the two phenomena to interact.
However I've never heard that a limerick pays attention to long and short syllables, only to stressed and unstressed. If it is true that a limerick is supposed to be written with attention to long and short syllables, I would be interested in who says so and why.