This book I believe would have been published within 1960-80. It was a collection of limericks and poems, black and white pictures only on rough pulpy paper, hardcover woven material,off white. No slip cover (sleeve) photo as I believe it likely had a slip cover at one time, but not once I had it as a child.
The illustrations, there was one for each, I think and they were very character based and they were all black and white. The very closest stories and illustrations that I can find that bear a resemblance is “Backward Bill” by Silverstein.
There is only one poem in the collection that I remember clearly. The illustration was of a skinny man walking on his hands in the sand. He has a pail hanging from his foot by the handle. The poem talks about this certain man collecting periwinkles on the beach and using his foot to carry the pail. I can’t remember the reason he has for doing this. I do remember it being a very comical book.
It would mean great deal if you were able to find this book. If there are any other details that come I can let you know.