It's a mess.
By RAW, Ghostly Grasp is completely nonfunctional most of the time. It works for ghosts and other incorporeal edge cases with a Strength score, though, and for them, it doesn't turn objects incorporeal by RAW. See the end for how.
The feat grants this effect:
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.
Seems straightforward enough, right? When I first posted an answer to this question, I thought so too, but then I was prompted to do more research, and the whole rules situation around this feat is a mess.
The incorporeal subtype was updated in the Monster Manual III's glossary (p. 214), to include the following passages, among other things:
Any equipment worn or carried by an incorporeal creature is also incorporeal as long as it remains in the creature’s possession. An object that the creature relinquishes loses its incorporeal quality (and the creature loses the ability to manipulate the object).
So! Normally, when an incorporeal creature picks up an object (somehow), it turns incorporeal with them. This is done through ghost touch weapons and similar effects in most cases, though there are a few others. Thankfully, these rules are not relevant here, because of Ghostly Grasp's statement that you "use corporeal items as though you were not incorporeal."
This means that when you are choosing to use the feat ("can"), you just ignore all of the incorporeal subtype's rules, including the part about turning objects incorporeal. However... when using items in this way, you run into some other rules.
Incorporeal creatures, by and large, have a Strength score of — (a nonability).
According to the rules for nonabilities, such a creature suffers from the following (MMIII, p. 217):
Strength: Any creature that can physically manipulate other objects has at least 1 point of Strength.
A creature with no Strength score can’t exert force, usually because it has no physical body (a prismatic golem, for example). The creature automatically fails Strength checks. If the creature can attack, it applies its Dexterity modifier to its base attack bonus instead of a Strength modifier.
So, while an incorporeal creature with Ghostly Grasp can use objects as if they were not incorporeal, they cannot exert force, nor can they physically manipulate other objects. That's a bit of a bummer. They don't even get a place on the carrying capacity table.
But hey, thanks to their Ethereal Plane weirdness, ghosts have a Strength score, despite being incorporeal! Or, more particularly, while manifested on the Material Plane, they are incorporeal, and per the incorporeal subtype, have no Strength score (despite having one):
It [an incorporeal creature] has no Strength score, so its Dexterity modifier applies to both its melee attacks and its ranged attacks.
Luckily, Ghostly Grasp lets our hypothetical ghost use corporeal objects as if they were not incorporeal... which means their Strength score applies, as that rule is no longer in the way.
Ghosts and similar beings who have the incorporeal subtype while retaining their Strength score on the stat block can use Ghostly Grasp to pick up corporeal objects. They will not turn said objects incorporeal when using them in this way.
Other incorporeal creatures, thanks to their Strength nonability, can take the Ghostly Grasp feat, but cannot exert physical force or lift objects at all. They likewise will not turn objects incorporeal when fruitlessly pushing on an object in this way.