I recently bought this guitar, it's a Korean 2000 Epiphone Les Paul

Information I found online:
model number: o00070136
July 2000
Production Number: 0136

I've tried it out on 2 different amps and the only way I can describe the sound from the guitar is nasally. I don't know if it's from the pickups or maybe from them sitting in there wrong.

What would you all suggest I do?

I'd start by leveling the pickups, readjusting their heights, spraying the pickup selector switch with contact cleaner, and cleaning the input jack by spraying a cable with contact cleaner and working it in and out a few times.
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when I think nasally I think the pickups are out of phase. But start with the pickup height. It may fix things. But I like the fact you tried more than one amp. Have you just purchased this guitar?

The only time I'd replace a pickup is if it wasn't loud or aggressive enough as I play metal mostly. Besides that I get just about every sound from my hands and the amps.
I did just purchase this guitar about a week ago. I'll try to level them out and do everything suggested.
1. Is this guitar "nasally" only when you have the pickup selector in the MIDDLE position, or all the time?

2. What amp are you using? How are you listening to these pickups?
I use it on an orange crush 10w amp and also behringer gm108 amp. This is my first electric so I'm fairly new with everything, I've had 2 acoustics before I got this. To me its nasally on all three positions especially when I strum the lower three strings.

I changed the heights to level them out and they still sound nasally.
That pickup needs to be setup properly, treble strings should be closer to the pickup and bass side strings further from pickup.

Get it setup properly and should improve a lot of things.