Interesting topic. Don Paterson has some poems in couplets without discernible metrical patterns and very loose off-rhymes or para-rhymes. Here's a
link to a poem entitled "11:00: Baldovan". As you can see the couplets are of varying length but the lines within the individual couplets tend to be of similar length. The effect is very different from Ogden Nash, if only because the rhymes are so faint, and because he doesn't play with the comic alternation of long and short lines within the couplet. However, one has the sense of a ghost of formal control over the material, which is quite effective. It certainly allows for a natural colloquiality, which is appropriate to the poem, as we are supposed to hear a small boy talking.