In DPP, it's a cinch! Open the (unedited) rom up in any hex editor - no need to decompress anything - and simply do a search for "00 05 05 00 08 05 0A 0A 05 0A 0B 05 0A 0C 14", @ pointer 0x1DE1B8, which, if i'm not mistaken, is located in one of the .bin overlay files (but i might be wrong, there. nevertheless, a simple search WILL turn up the correct result).
it works like this: 00 (Normal) attacks 05 (Rock) and does 05 (50%) damage, 0A (Fire) attacks 0C (Grass) and does 14 (200%) damage, etc. Neutral hits (Ghost vs. Fire, for example) aren't shown, but are simply "default," blank, no entry.
00 - Normal
01 - Fighting
02 - Flying
03 - Poison
04 - Ground
05 - Rock
06 - Bug
07 - Ghost
08 - Steel
09 - ???-type
0A - Fire
0B - Water
0C - Grass
0D - Electric
0E - Psychic
0F - Ice
10 - Dragon
11 - Dark
I've already deduced, like I posted long ago, that the type chart isn't present (uncompressed, at least) in this form in HGSS. I even checked for other orders, by searching for "0A 0A 05," one-by-one, without any luck.