Use A-Text, there are 9 strings that make up his entire intro speech. They are located at the following, in order:
here's a pic of what it looks like with the default palette for it.
TL;DR is there any way to get the right palette for this?
(btw, i've already tried using the Next Pal and Previous Pal buttons, and all the palettes that load don't look like they are for oak.)
I don't think the palette that Oak uses in the intro is unLZ compressed, at least Birch in Ruby/Emerald isn't, so I don't think it will be found in unLZ. You can use VBA's palette viewer and APE's search feature to pinpoint the offset where his palette is. Since the image is 256 colors it can be a bit tricky to find, which is why the offset hasn't been posted around here.
The games simply uses the "giveitem" command followed by "end". Place that script in the Pokeball OW sprite on your map and it should work.