if anyone could give me some pointers, that would be uber.

Whenever you catch yourself typing the same expressions more than two times, give it a break and think: "Can I somehow express this in a loop?". In this case the outcome of such a thought would look like this code.

use strict;

my @haiku = 
(
    [
        'annoying sensei',
        'oh, young grasshopper',
        'dis-honourable',
        'you aburi brain'
    ],
    [
        'learn to run before you walk',
        'he thinks he knows everything',
        'insubordinate pupil',
        ],
        [
        'hey, wait a minute',
        'he must be senile',
        'he will face my wrath',
        'his brain is not well'
    ],
);

for my $line (0..2)
{
    print $haiku[$line][rand @{$haiku[$line]}], "\n";
}
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Here we have a data structure (array of arrays) that holds your haiku strings. Once we have that we can easily loop over the main array an choose a random line from each "sub-array". See perlref and perlreftut for more about data structures.