A ghost with Ghostly Grasp making a strength check?

Question

A ghost is incorporeal and thus has no strength and normally cannot manipulate things on the material plane, however with the Ghostly Grasp feat ( Libris Mortis: The Book of Undead, p. 27) You can manipulate objects, the problem is you have no strength score.... :

Ghostly Grasp

You can handle corporeal objects even while incorporeal. Benefit

You can wear, wield, and otherwise use corporeal items as though you were not incorporeal. Special

Without this feat, an incorporeal creature can only wear or wield items that have the ghost touch special ability.

So if you have to catch a falling character, lift a heavy item, make an opposed strength check to tug of war etc. How is this resolved?

Answer 1

Ghosts still have a strength score. The only ability they don't have is constitution. Just use their assigned strength for this purpose.

From SRD page on Ghosts:

Abilities

Same as the base creature, except that the ghost has no Constitution score, and its Charisma score increases by +4.

Also, note that while a ghost does get the incorporeal subtype, it is not always an incorporeal creature. Their Manifestation ability grants incorporeal status on the material plane only:

Manifestation (Su)

Every ghost has this ability. A ghost dwells on the Ethereal Plane and, as an ethereal creature, it cannot affect or be affected by anything in the material world. When a ghost manifests, it partly enters the Material Plane and becomes visible but incorporeal on the Material Plane. A manifested ghost can be harmed only by other incorporeal creatures, magic weapons, or spells, with a 50% chance to ignore any damage from a corporeal source. A manifested ghost can pass through solid objects at will, and its own attacks pass through armor. A manifested ghost always moves silently. A manifested ghost can strike with its touch attack or with a ghost touch weapon (see Ghostly Equipment, below). A manifested ghost remains partially on the Ethereal Plane, where is it not incorporeal. A manifested ghost can be attacked by opponents on either the Material Plane or the Ethereal Plane. The ghost’s incorporeality helps protect it from foes on the Material Plane, but not from foes on the Ethereal Plane.

The ability scores for a ghost are defined in the monster manual (the primary source for monsters), and those ability scores include strength. Additionally, the ghost has specific rules that explicitly state that it is not incorporeal on the ethereal plane. As such, the ghost normally possesses a strength score with the sole exception of when it is manifests on the material plane, and even then it still possesses its strength score on the ethereal plane. It has specific rules that clearly take precedence over the general rules for the incorporeal subtype.

If more evidence is required, look at the following abilities also from the ghost template:

Corrupting Touch (Su) A ghost that hits a living target with its incorporeal touch attack deals 1d6 points of damage. Against ethereal opponents, it adds its Strength modifier to attack and damage rolls. [emphasis added] Against nonethereal opponents, it adds its Dexterity modifier to attack rolls only.

Draining Touch (Su) A ghost that hits a living target with its incorporeal touch attack drains 1d4 points from any one ability score it selects. On each such successful attack, the ghost heals 5 points of damage to itself. Against ethereal opponents, it adds its Strength modifier to attack rolls only. [emphasis added] Against nonethereal opponents, it adds its Dexterity modifier to attack rolls only.

Answer 2

It uses Charisma

The operative phrase is "as though you were not incorporeal."

Any creature that becomes incorporeal has no strength score (SRD, Incorporeal Subtype):

It has no Strength score, so its Dexterity modifier applies to both its melee attacks and its ranged attacks.

On the Material Plane, but not on the Etheral, a ghost is incorporeal, so it follows that it never has a Strength score while on the Material Plane (SRD, Ghost, Emphases mine):

Manifestation (Su): [...] When a ghost manifests, it partly enters the Material Plane and becomes visible but incorporeal on the Material Plane. [...] A manifested ghost remains partially on the Ethereal Plane, where is it not incorporeal. A manifested ghost can be attacked by opponents on either the Material Plane or the Ethereal Plane. The ghost’s incorporeality helps protect it from foes on the Material Plane, but not from foes on the Ethereal Plane.

Corrupting Touch (Su): [...] Against ethereal opponents, it adds its Strength modifier to attack and damage rolls. Against nonethereal opponents, it adds its Dexterity modifier to attack rolls only.

Draining Touch (Su): [...] Against ethereal opponents, it adds its Strength modifier to attack rolls only. Against nonethereal opponents, it adds its Dexterity modifier to attack rolls only.

You can see that the "[...] Touch" abilities use the same rules as the incorporeal subtype for attacks. So, on the material plane, a manifested ghost is incorporeal and thus has no Strength score.

The Rules for Corporeal Incorporeality

Libris Mortis, page 143 has a section on "Losing Incorporealness" Which says, in regards to a Strength score:

The now-corporeal creature gains a Strength score equal to its Charisma score (not including any nonpermanent modifiers to Charisma, such as an eagle’s splendor spell). Its incorporeal touch attacks become normal touch attacks (and it uses its Strength modifier on attack rolls unless it has Weapon Finesse).

A ghost, or any incorporeal creature, using the benefit of ghostly grasp to 'wear, wield, and otherwise use corporeal items as though [it] were not incorporeal', would 'lose incorporealness' relative to those objects and have a Strength equal to its permanent Charisma in regards to those objects.

Rules Compendium p. 64-5, under the "Attacks" heading, has a similar rule for incorporeal creatures interacting with other incorporeal creatures, and rules about not being able to interact with corporeal creatures:

An incorporeal creature can’t trip or grapple, nor can it be tripped or grappled. In fact, it can’t perform any physical act that moves or manipulates a corporeal opponent or that foe’s equipment, nor is it subject to such acts. An incorporeal creature that attempts to grapple or move another incorporeal creature or object uses its Charisma modifier for rolls on which a Strength modifier normally applies.

Ghostly grasp, in permitting the use of items (objects), permits the incorporeal creature to ignore the "or that foe's equipment" clause, and interact as if corporeal with it, such as attempting to disarm them, using Charisma where Strength would otherwise be used.

Additionally, for creatures that wear clothing and/or armor, the incorporeal creature might even be able to trip or grapple them. Or even try to catch them when they're falling...