Do specific creatures/types of creatures have weaknesses to specific types of attacks?

Some creatures are weak to different forms of magic, and it follows the normal fantasy archetypes:

• Frost-based creatures are weak to fire, but resistant to frost
• Fire-based creatures are weak to frost, but resistant to fire

Notably, this elemental-based dichotomization affects dragons and Atronachs.

There are also creatures that are not elemental-based, but are resistant to their natural surroundings:

• Goats, snow foxes, and mammoths are resistant to frost
• Chauri (the giant insects) are naturally resistant to poison

Vampires are resistant to frost, but weak to fire as well.

Automata and some undead are immune to poison and resistant to frost: this includes the Dwarven automata and the Draugr.

Spriggan are weak towards fire, as are trolls (a common fantasy trope).

Giants are resistant to magic of all forms.

As Skizzlefrits notes in the comments, while many foes won't have inherent elemental weaknesses, the side effects of each elemental class makes them suitable against different types of enemies:

• Shock spells are useful against mages because they drain magicka in addition to health
• Frost spells are useful against warriors because they drain stamina in addition to health
• Flame spells are useful against groups because they deal area-of-effect damage and/or damage over time

I'm not aware of the type of weapon (bludgeoning, piercing, or slashing) affecting damage to an enemy. If I remember correctly, the type of weapon didn't affect anything in Oblivion or Morrowind, either: it's not a mechanic used in the Elder Scrolls series.

In terms of where to find this, I pulled the list above from the strategy guide's bestiary, but they all should make sense from a common sense perspective (or at least a common sense perspective within a high fantasy setting). I wouldn't be surprised if there were books that cover some of them.

I'm pretty sure that, as in oblivion, all forms of daedra are weak to the shock school of magic. So if you are looking to get those daedra hearts to make the armor I would keep that in mind... On a personal note I prefer lightning, as it is inherently more bada$$

Vampires are weak to fire spells and effects. One of the load screens tells you this, and it's been the case at least since Morrowind.