What is the difference between ever with perfect tense and past tense?
I'm the queerest young fellow that you ever heard. (related link)
I'm the queerest young fellow that you've ever heard.
In this case, there is no semantic or syntactic difference. In formal registers, the perfect construction is preferred here because it makes it clear that the hearing extends all the way up to the moment the song is sung, whereas the past form implies that the hearing ended at some point in the past. But colloquially, either may be used.
As snailboat points out, euphony governs here—specifically, metrics. Note that the original has the inversion "ever you heard", not "you ever heard". The meter employed in this drinking-song is the very jaunty "anapaestic tetrameter": each line has four 'feet' of three syllables, only the last of the three being stressed. Musically and poetically this mesure permits omission of an occasional unstressed syllable, but the effect is stronger if you adhere strictly to form, and it's badly damaged if you put the stress on a syllable which would be unstressed in ordinary speech. Consequently, Gogarty employs the inverted simple past, which fits the meter perfectly:
˘ ˘ ¯ ˘ ˘ ¯ ˘ ˘ ¯ ˘ ˘ ¯ I'm the QUEERest young FELlow that Ever you HEARD