Casting greater mighty wallop without a spellcasting class
You can... but it’s heavy, heavy cheese, not just “oh, you’re a 12th-level undead initiator? sure, you can have some spells.” And it may not be possible without ret-con or heavy psychic reformation, since a couple of the feats are 1st-level-only.
The typical approach to getting class-less spellcasting is the Magical Training feat from Player’s Guide to Faerûn, which is a Regional feat (i.e. only available at 1st level), and requires you to be an elf from Evereska or Evermeet or a human from Halruaa or Nimbral. Outside Faerûn, it may be unavailable entirely, adapted to other regions, or the whole regional thing might be dropped entirely: you would have to ask your DM.
From there, you can take the Precocious Apprentice feat from Complete Arcane (page 185, not in the feats chapter). This is another 1st-level-only feat. It allows you to learn a 2nd-level arcane spell, and to get a single 2nd-level spell slot to cast it per day.
Combine that with the Sanctum Spell metamagic feat, also in Complete Arcane, which lets that 2nd-level spell count as a 3rd-level spell while in your designated sanctum, so that you “count as” being able to cast 3rd-level spells. Then you can activate the Dragonsblood Pool magical location from Complete Mage (it’s probably best to designate the pool as your sanctum, so you are able to cast a 3rd-level spell at the time you activate it). Now you have a 3rd-level spell slot per day for a whole year.
Note that absolutely none of this has anything to do with your HD, type, or classes. With enough feats, you could do this from 1st level.
If you wanted a divine spell, the Mad Faith feat from Heroes of Horror would replace Precocious Apprentice, Sanctum Spell, and the Dragonsblood Pool, and would leverage your undead type. It can get you a 3rd-level divine spell slot if you have severe depravity—and depravity does nothing bad to an undead creature. But, of course, Mad Faith requires 1st-level divine spells, and Magical Training doesn’t work on for those, and in any event greater mighty wallop is not found on any divine spell lists.
As for actually getting greater mighty wallop, that’s easy—Magical Training allows you to choose wizard as the spellcasting class you cast spells like. That means you can just scribe it into your spellbook the same as any other wizard. Wizards are even allowed to scribe spells they can’t cast yet, so there’s no awkward concern about the order of operations here.
Boosting caster level
This is harder. You might be able to use Practiced Spellcaster (you cast like a wizard—does that go far enough that you could select wizard as your class with Practiced Spellcaster? probably not...), but even if you can that only gets you to caster level 5th.
For the same reasons, you probably can’t use a prestige class either. I mean, you qualify for jade phoenix mage, and it would continue to advance your initiator level and maneuvers, but you (almost-certainly) won’t be able to actually apply the spellcasting progression against anything. But if your DM somehow accepted all of the above, maybe they’ll also buy that you count as a 0th-level wizard or something and jade phoenix mage can “stack” with that? Extremely dubious.
If those are out, and they almost-certainly are even RAW, we’re left with just nickel-and-diming everything. An orange ioun stone, some reserve feats, a prayer bead of karma maybe.
Oooor... we could just cheese caster level, too. There are numerous infinite caster level tricks out there. We could continue the spellcasting cheese (more feats, it can literally go right up to 9th-level spells) to get greater consumptive field and then pour oil down an anthill, for example.