So, I was planning on installing these mods to IWD:

Fixpack
Tweak pack
NPC mod
Widescreen mod

Can anyone please tell me the correct order to install? Are these mods compatible?

Did you check the Mod Guide sticky?

Yes, but I didn't see anything that answers to this question.

I'm halfway through the game using those mods without any problems.

The order I installed them was:
Fixpack
Tweak pack
Widescreen mod
NPC mod

Actually, it does. It says "Best installed in this order except where noted" and goes on to order them (for what you've listed):

1) Widescreen Mod
2) NPC mod (Best installed before Tweak Pack.)
3) Fix pack
*Note: the Fix pack is recommended instead of the Tweak pack, as it replaces and incorporates the components of the Tweak Pack, from what I understand.

*edit* Or, you could install in the order Warmark did...

Ah, somehow I missed that. Thanks for pointing it out. Oh, so having both of them is unnecessary. I see.

Yeah, I think so. Sorry I'm not totally positive. My install is fairly old and I used the old Tweak pack, but not the Fix pack. But I think the Fix pack just incorporates most of the good Tweak stuff anyway,

If memory serves, I installed them in the order shown in the guide (Widescreen, Unfinished Business, Tweak Pack) I don't have the NPC mod installed.

Actually this quote is from the Icewind Dale Fixpack page that I used: "This originally started as a component of the IWD Tweak Pack, but was broken out in to its own mod because 1) it's gotten fairly extensive on its own and 2) it should be installed right after the official patches whereas the tweaks should be last installed" and that's how I installed it as I said earlier.

And Also from the NPC mod Readme: mods may overwrite IWD NPC. As such, it is recommended
to install IWD NPC after them.

Fix Pack
Unfinished Business
Item Upgrade
IWD NPCs
Tweak Pack
Widescreen Mod

For IWD the Fixpack should always be first, the Tweak pack next to last. I believe WSM is recommended last by DavidW.

And if you're up for a challenge, check out IWD-in-BG2. It's an advanced BETA, but pretty close to fully complete. It's also at G3.

Yes, this would be my recommendation for install order as well. Tweaks wants to be last so that it can modify items/creatures/etc. added by other mods (and hence why Widescreen after it will be just fine). Fixpack wants to be first so that later mods will clone fixed items/creatures/etc.

The middle is always the murky bit; I've written UB and IU to work regardless of order. I'm pretty sure IWD NPC doesn't really care either, though it might add/change content for the new quests, so put it after those two. This warning exists on pretty much all IWD mods due to Auril's Bane. It's an old mod and overwrites pretty much every file it touches; newer mods patch files and co-exist a lot better.