This question has opened a Pandora's Box in my head. The first answer (and resultant discussion) states that warlocks are unable to learn invocations described in prestige class descriptive text because they are not on the warlock invocation list and should be treated as class features. However, if you look at the Eldritch Disciple prestige class (CM p.53) you will see where there is a class feature designed that takes the place of an eldritch essence without being an eldritch essence (see Gift of the Divine Patron (Su) - Healing Blast on p.54).
Then there is the Eldritch Theurge prestige class (CM p.57). It specifically states in the descriptive text that "All eldritch theurges have levels in the warlock class" since only warlocks level both invocations and have eldritch blast. Additionally, it does not grant the ability to cast any new types of invocations:
Invocations: At each level, you gain new invocations known and an increase in caster level as if you had also gained a level in an invocation-using class to which you belonged before adding the prestige class level. (This includes eldritch blast.) You do not, however, gain any other benefit a character of that class would have gained. If you had more than one invocation-using class before becoming an eldritch theurge, you must decide to which class to add each level for the purpose of determining caster level and invocations known.
At levels 3 and 10, it grants bonus invocations in addition to the invocations that would be earned through invocation-class progression. Those are Spellblast, defined as a Lesser invocation, 4th-level equivalent, Eldritch Essence, and Greatreach Blast, defined as a Greater invocation, 5th-level equivalent Eldritch Essence.
There are additional invocations defined and granted for the Enlightened Spirit (CM p.61).
Also note that all of these invocations are listed by WoTC on their official Invocation Index
The summary and root of the question is this: Is a warlock not able to learn these invocations despite the fact that they are designed as invocations with lesser/greater/etc. status instead of class abilities (as the same book did with the healing essence-like class ability)? Is there any actual rule stating that these invocations are not, in fact, usable by warlocks? It appears to me that much like feats that are defined in a prestige class description, any warlock who is able to learn least/lesser/greater invocations, as applicable, should be able to learn these. It's just that members of these prestige classes additionally get the invocations as bonus invocations instead of through standard warlock invocation progression. Otherwise, if these features were to be granted only as class features, why would they be designated as least/lesser/greater?