The major form preceding Noh was gigaku, a kind of masked drama brought to Japan from Korea and China in the Seventh Century. This was generally light-hearted farce with erotic elements. Masks for this date back to at least the Eighth Century. Rather like Noh masks, they were often more caricatured.
There is a lengthy tradition of itinerant storytellers: this was mentioned under Bunraku, but they didn't all work with puppets. Some would show a series of drawings or prints as the accompaniment to their narration. Some claim that this is one of the reasons why comic books became so widely appreciated in Japan, but really it is simply part of a tradition of combining images and words in narrative going back over a thousand years.
One other form I want to mention: by the early 19th Century in Edo, there were people on stage reciting what were called "punch-line stories", which sounds rather like stand-up comedy; and sometimes comedy stories made up on the spot from three topics called out by the audience, which sounds very like improv.