Technically skeletons and zombies can be ordered to imbibe fluids (in the case of skeletons the fluid would flow over the bones), so: can skeletons or zombies can use and benefit from potions?
The general rules for potions only say this on the subject:
A creature must be able to swallow a potion or smear on an oil. Because of this, incorporeal creatures cannot use potions or oils. Any corporeal creature can imbibe a potion or use an oil.
So it seems that the answer is Yes, they can.
You can argue that some corporeal but mouthless creatures won't be able to benefit from a potion - and this sounds like a sensible houserule...
5\$\begingroup\$ The undead type says that "[u]ndead do not breathe, eat, or sleep," and the only creature that don't specifically drink are those with the kami subtype (whether this means kami still can is something else). The undead type's nonlethal damage immunity makes dying of thirst nonissue, but undead creatures can totally hit the pub (or potion bar? Is that a thing?) just like anyone else. \$\endgroup\$ Sep 11, 2014 at 11:26
1\$\begingroup\$ But the bones of a skeleton are physical, so really they could be smeared with oil... \$\endgroup\$– PaulSep 11, 2014 at 13:00
The necromancy spell Deathwine has a reference to undead drinking potions:
In addition, any undead creature (or other creature healed by negative energy) that drinks a potion affected by deathwine is healed of 1d8 points of damage.
It seems to me that if any rule in the canonical rule set refers to a specific action then the rule set explicitly condones that action. Therefore undead are allowed to drink potions, and because it refers to undead generally rather than specifying types of undead, undead are generally allowed to drink potions unless exceptions are made elsewhere in the rule set.
\$\begingroup\$ Also, in case it changes anything: Deathwine is from the Rise of the Runelords Anniversary Edition adventure path. See the copyright notice at the bottom of the spell description (ctrl+f 'copyright notice' if you can't spot it) \$\endgroup\$ Sep 15, 2014 at 1:59
\$\begingroup\$ You're welcome; and welcome to the site! Since you have 20 rep, you can join us in chat now if you wish. \$\endgroup\$ Sep 15, 2014 at 2:07
The SRD says
A potion is a magic liquid that produces its effect when imbibed. Magic oils are similar to potions, except that oils are applied externally rather than imbibed
Since all that is required is imbibing and not digestion, and they apply immediately upon imbibing. then undead can use them.
Furthermore, even if your QM rules that that they can't, you can just point them at oils. Oils use the craft potion feat, can contain any spell below level 3 (just like potion), and are triggered by rubbing them on something instead of imbibing. I doubt anyone would argue that you cannot rub an oil on a skeleton.
The difference between imbibing and digesting is the problem. What must be assumed in many cases is a zombie is both corporal and incorporal. Sometimes the skeletons, adventures run across have been ordered to scatter their bones into piles as traps. Which pull themselves back together when their orders are triggered. If the potion effects bones I would say yes, for skeleton. Zombies are often cast from the same spell so assume that zombie are both. In this case I would assume any oil or potion that would affect leather. Next problem if a potion requires a choice this choice would require addition to total orders. I don't want you to miss understand because once the potion is digested its magic is spread via the very non corporeal magic.
3\$\begingroup\$ This information is based on absolutely nothing. Nowhere in the rules does it even mention digesting. \$\endgroup\$– TheikSep 12, 2014 at 11:30
\$\begingroup\$ Especially since making digestion an issue would turn instant-effect healing potions into something more like "have a drink and a lie-down for an hour or two". Not that it wouldn't make for interesting play, but that's not as Pathfinder plays it, now is it? ;-) \$\endgroup\$– DevSolarOct 21, 2014 at 13:19
\$\begingroup\$ @Theik That's not entirely true \$\endgroup\$ Feb 15, 2015 at 2:48
\$\begingroup\$ @thedarkwanderer I meant digestion being required for potions affecting you or not, not monsters who have digestion as flavour abilities. ;) \$\endgroup\$– TheikFeb 17, 2015 at 8:50