When Nash wasn't writing poems, he made guest appearances on comedy and radio shows and toured the United States and the United Kingdom, giving lectures at colleges and universities.
Nash was regarded with respect by the literary establishment, and his poems were frequently anthologized even in serious collections such as Selden Rodman's 1946 A New Anthology of Modern Poetry.
Nash was the lyricist for the Broadway musical One Touch of Venus, collaborating with librettist S. J. Perelman and composer Kurt Weill. The show included the notable song "Speak Low". He also wrote the lyrics for the 1952 revue Two's Company.
Nash and his love of the Baltimore Colts were featured in the December 13, 1968 issue of Life, with several poems about the American football team matched to full-page pictures. Entitled "My Colts, verses and reverses", the issue includes his poems and photographs by Arthur Rickerby. "Mr. Nash, the league leading writer of light verse (Averaging better than 6.3 lines per carry), lives in Baltimore and loves the Colts", it declares. The comments further describe Nash as "a fanatic of the Baltimore Colts, and a gentleman". Featured on the magazine cover is defensive player Dennis Gaubatz, number 53, in midair pursuit with this description: "That is he, looming 10 feet tall or taller above the Steelers' signal caller...Since Gaubatz acts like this on Sunday, I'll do my quarterbacking Monday." Memorable Colts Jimmy Orr, Billy Ray Smith, Bubba Smith, Willie Richardson, Dick Szymanski and Lou Michaels contribute to the poetry.
Among his most popular writings were a series of animal verses, many of which featured his off-kilter rhyming devices. Examples include "If called by a panther / Don't anther"; "Who wants my jellyfish? / I'm not sellyfish!".