There doesn’t seem to be a lot of info about this form other than the basics, from what I can find, but that might be because of its purpose and why dodoitsu are written.
The themes for dodoitsu are of love or work life, and are meant to be humorous. In total, there are 26 syllables (“on” in Japanese) with four lines that are 7-7-7-5; the syllable count could also be less. This form was originally used as form of folk verse, something a bit more lighthearted and less serious or thought-provoking.
Here’s a bit of a modern, English example that I like. It’s called “prep-dodoitsu” by deinktvis on DeviantArt; he decided to shave down two syllables per line (5-5-5-3):
with knife in hand,
i face the onslaught;
woe be unto you,