"Tusk" has odd instrumentation but a propulsive rhythm and earwormy hooks, and "They're Coming to Take Me Away" is a novelty song, which were wild cards on Top 40. I would say that a weirder one is Bob Dylan's "Rainy Day Women #12 and 35." At least the brass band on "Tusk" is tight; what's a drunk Salvation Army Band doing running a song up to #2? Especially with a particularly atonal lead vocal by a voice many people notoriously can't stand, intoning lyrics that aren't funny exactly, more just weird and mildly unpleasant? It's not like Dylan was an established hitmaker as a recording artist; he'd had only two Top-10 singles prior to this and would have only two more ever, and "Like a Rolling Stone" was his only single that ever charted higher, and then only marginally:
http://www.expectingrain.com/dok/cd/dylancharts.html. The song did get some publicity from being called out for drug references, but a lot of people must have liked it for
something more than the chance to hear a singer say "get stoned" out loud.
(Full disclosure: Bob Dylan is by some distance my favorite popular musician ever. "Rainy Day Women #12 and 35" is one of only a small handful of songs he recorded prior to 1969 that I just don't like much.)