Our warlock is grappled by a black pudding.
There is a second black pudding standing in an adjacent square, currently not involved in the grapple.
If the warlock activates his Eldritch Blast (Sp) to attack the ooze he is grappled with, will either/both of the two oozes get an attack of opportunity on him?
A creature that attempts to activate a spell-like ability—like the warlock invocation eldritch blast (Complete Arcane 7)—while it's grappled exercises the grapple option cast a spell (Player's Handbook 156) because spell-like abilities "are magical and work just like spells" (Monster Manual 315) and because "[u]sing a spell-like ability… works like casting a spell…" (PH 142).
With this in mind, a warlock must possess the feat Sudden Still (CAr 83) to even consider activating any of his invocations (like eldritch blast) while in a grapple because "somatic components [are] required for warlock invocations" (CAr 7), and while grappled a spell can be cast (and, likewise, a spell-like ability can be activated) only if "it has no somatic component" (PH 156). (The warlock is very nearly unique in his need here for the Sudden Still feat: most spell-like abilities simply have no components at all!)
Thus the grappled warlock must first employ the benefit of the feat Sudden Still so as to enable him to make a Concentration skill check to activate the spell-like ability eldritch blast (DC 21). Failure means that the blast fails. Success means that the warlock activates the eldritch blast; because the warlock activated a spell-like ability, he provokes attacks of opportunity from opponents who threaten him—in this case, that's the black pudding that's not grappling him. (The black pudding that's grappling the warlock doesn't also threaten an area unless it's used its special ability improved grab to suffer a −20 penalty on its grapple check to grapple the warlock.)
The warlock can try to activate that spell-like ability by casting on the defensive (also see PH 142), attempting to avoid provoking attacks of opportunity for the spell-like ability's activation by making a second Concentration skill check (DC 16) after succeeding on the first. Failure on this second Concentration skill check also means that the blast fails. Success means that activating the spell-like ability provokes no attacks of opportunity. Alternatively, as this answer mentions, a warlock that possesses the feat Quicken Spell-like Ability (eldritch blast) (Monster Manual 304) could opt to use that feat's benefit to employ the blast as a swift action so that its activation doesn't provoke attacks of opportunity. (Casting a quickened spell doesn't provoke attacks of opportunity therefore neither does activating a quickened spell-like ability.)
Finally, the warlock provokes attacks of opportunity from all opponents who threaten the warlock for making a ranged attack using the blast. (This likely won't matter if the oozes are the only opponents—most oozes have Intelligence as a nonability therefore they don't gain feats so they won't usually have, for example, the feat Combat Reflexes (PH 92); the ooze outside the grapple will probably make its attack of opportunity when the warlock activates—rather than attacks with—the blast.)
This is, obviously, enormously complicated… and not a whole lot of fun. (Seriously, only the most paranoid or feat-rich warlock takes the feat Sudden Still of all things!) A DM that allows the warlock to just go ahead and blaze away with his blast while the warlock's grappled yet only provoke attacks of opportunity for activating the spell-like ability and making the ranged attack does the warlock's player—and, perhaps, all the players, including himself—a tremendous favor.
Note: A stricter reading forbids entirely activating a spell-like ability while in a grapple as use a spell-like ability just isn't an option If You're Grappling, but this DM urges If You're Grappling not be read as an exhaustive list of options! Also, that spell-like abilities are treated like spells while a creature is in a grapple is confirmed (yet consider the source) by the Rules of the Game Web column "All about Grappling (Part Two)" by D&D 3e co-designer Skip Williams. In addition, Complete Arcane errata gives the typical eldritch blast a spell level of 1, but this spell level can be higher; this answer assume the typical blast for convenience. Finally, be sure your next PC (or this one if he survives) has from the Magic Item Compendium an anklet of translocation (71) for situations just like this; it's probably the best 1,400 gp your PC will ever spend.
An Eldritch Blast is a spell-like ability. Using a spell-like ability provokes from all who threaten. You do not threaten while engaged in a grapple. Therefore, the activation of the Eldritch Blast would provoke from second ooze. However, a black pudding has Improved Grab, which means it can take a -20 on grapple checks and not be considered grappling. If the first black pudding is doing so at the time, then the blast would provoke from both.
Once for being a spell-like ability (“Using a spell-like ability while threatened provokes attacks of opportunity.”), and again because eldritch blast is a ranged attack (“Attack (ranged) Yes” in Table: Standard Actions).
A warlock’s invocations are spell-like abilities; using an invocation is therefore a standard action that provokes attacks of opportunity.
Eldritch Blast (Sp):
Both on page 7 of Complete Arcane.
Their stat block gives them a 10-ft. reach, and nothing in their description bars them from threatening or making attacks of opportunity.
Grappling Consequences
While you’re grappling, your ability to attack others and defend yourself is limited.
No Threatened Squares
You don’t threaten any squares while grappling.
This means that the black pudding actually grappling you may not be able to actually take the attack of opportunity. The other black pudding, however, absolutely would.
One of the special attacks listed in the black pudding stat block is improved grab, and that includes a rule saying
The creature has the option to conduct the grapple normally, or simply use the part of its body it used in the improved grab to hold the opponent. If it chooses to do the latter, it takes a −20 penalty on grapple checks, but is not considered grappled itself; the creature does not lose its Dexterity bonus to AC, still threatens an area, and can use its remaining attacks against other opponents.
So the black pudding grappling you had the option of continuing to threaten your warlock, if it could win the grapple check with a −20 penalty.
You provoked two attacks of opportunity. As black puddings are mindless (unless they somehow weren’t, but that’s unlikely), they cannot gain feats, so they could not have the Combat Reflexes feat necessary to take both, but nonetheless there were two provocations. The black pudding nearby absolutely threatened you and could make one attack of opportunity against you. The one grappling you may or may not have threatened you, and so may or may not have been able to make the attack of opportunity.
If these had been other creatures who did have Combat Reflexes, and they were using the −20 option on improved grab, then you could have easily taken 4 attacks of opportunity here.
I. All warlock invocations have a somatic component. Without removing that limitation, such as via the Sudden Still metamagic feat, a warlock is incapable of using an invocation in a grapple.
II. Using a spell-like ability is treated identically to casting a spell. So if a warlock works around the problem from (I), then one has two options to then avoid provoking an attack of opportunity for casting a spell while threatened: Quicken Spell-Like Ability since quickened spells do not provoke attacks of opportunity, or casting on the defensive. (note that quicken spell-like ability only helps avoid attacks of opportunity from spell casting. One must still find a method to remove somatic components)
Touching an opponent with a touch spell is considered to be an armed attack and therefore does not provoke attacks of opportunity.
It then goes on to clearly define that this rule applies to both ranged and melee touch attacks:
Touch attacks come in two types: melee touch attacks and ranged touch attacks.
CONCLUSION
A warlock who manages to cast Eldritch Blast defensively or quickened will not provoke an attack of opportunity. Managing to cast it otherwise provokes a single attack of opportunity due to casting a spell while threatened.
