I'll try a different tack, since there seems to be a pattern going on in the sketches:
In the order which I noticed them: The final one seems to have two similar parts:
easter eggs / stir eggs
The third one as well
half-life / half-life (or is it maybe "X-ray Ray" instead?)
and the title and the first image too:
Island (sketch) / I-land sketch
Following the pattern, the second one is probably
eclipse clips
the fourth looks like
eyeshadow shadow
The pasta bowl still eludes me, but stitching together the differences between the parts (as they are pronounced), and ignoring the first one as it's claimed to be for flavour only, we get
E-?-I-?-E
So trying to fit a plausible reason for being on an island to that pattern, the pasta sketch must then be
Bow bowl ("Bow pasta" - "Elbow pasta" works even better, as pointed out by Deusovi in the comments)
And the radiation person probably is called Ray,
( EDIT: nofinally got it, he isn'tthat's not Ray, that's obviously an
Exterminator terminator!
)
which would addall adds up to the final reason for your trip being that
you were EXILEd.