Gimmicky undead? Check.
Descriptive name? Check.
Cripplingly high HD count? You bet.
The deathshrieker is a delightful medium-sized undead with -cough- eighteen hit dice. It's main assets are incorporeality, a (weak) charisma-draining touch, okay ability scores, and a number of flavorful special abilities.
Said abilities include the passive paralyzing Despair (actually a pretty decent save-or-suck, I gotta admit), the unique but mostly irrelevant Silence Vulnerability (makes it hard for the Deathshrieker to enter or stay in areas of Silence), and the reasonably neat Death's Grace (which will amount to a flat +6 profane AC bonus in most games, which is just fine).
Death Rattle is an ability that is a moderate hindrance on a monster, and barely worth acknowledging on a PC. Dying isn't something most player characters can afford to do a lot, especially not undead ones.
Finally, there's Scream of the Dying, which is... underwhelming. When I first saw the Deathshrieker's general theme and HD, I figured it had to have an ability based on Wail of the Banshee, or something similar. I mean, I've seen WotC monsters: giving an 18 HD monster a single 9th-level spell and calling it balanced seemed like the thing they'd do.
Instead, the ability allows the Deathshrieker to create either a cone or a spread of horrible shrieks once per day, with slowly intensifying effects, going from deafness to stunning to insanity.
Now, this already seems like a pretty average save-or-lose, with many monsters and virtually all casters being capable of causing either effect without having to waste a turn first. However, it actually gets worse: any creature that's deafened (like, I don't know, anyone who failed the first saving throw) gets a bonus on the saving throws that are actually important. That's right: it's a save-or-lose that first makes you spend a turn buffing your foes' saves. Also, the ability isn't friendly, because of course it isn't.
Given their lack of advancement options, average chassis, and general horribleness, I think -0 LA is the only assignable LA here.
No, seven more HD don't change anything here. -0 LA.