Besides what the origin comic might say, are there any theories on what those dark crystals of King Sombra are, or what they do?

Just curious!

I really don't like Sombra's origin story because it sez he's not even a real pony!

As to your query, I'd say the dark crystals are Sombra's dark magical energy in solid form, like the mana of his dark magick can coalesce into physical matter and be shaped however Sombra wants but unless he's deliberate they resemble chaos (no real sensible form, so they fall back on a form resembling thorns or broken glass)

There's no telling what they can do since dark magic is associated with evil, and evil thrives through deceit and treachery. Sombra could make his dark crystals do whatever is within his power, like how he made the ones that showed Twilight and Spike their personal fears, but with a little imagination they could do virtually anything.

4257162 Rushed and "meh" non-canon (to the show) comic aside (don't get me wrong, I love the IDW comics in general), I would imagine they serve a largely martial purpose for him. Wherever they spring up, they seem to corrupt and change the land around them, and with this change could bring about powerful enchantments and residual dark energies that could be used as additional power sources for Sombra and whatever army he could potentially muster for an occasion.

If the crystals can act as essentially dark magic "batteries" they could be useful as siege instruments, traps, offensive weapons, tools for dark magical research, magical support for Crystal Empire architecture (a dark variant of it), enchanting, and more.

I have imagined that Sombra´s talent has something to do with those crystals. As in, what he really liked was working on these things, you know, like a making them into sculptures, statueettes or whatever. As long as it was crystal, he could make it.
Then of course, fate intervenes, and when he, so to say, "Falls to the Dark side" the crystals turn black.

4257162 I always thought his Dark Crystal Magic to be a form of manipulation. We've seen him ride his crystal pillars in the show, so I would imagine he used them as platforms, especially to combat the Princesses since they've got flight over him. He could likely also imprison ponies in crystal much like how he 'killed' Amore in the comic.

More so than that, we know that Dark Magic in it of itself causes Dark Crystals to sprout. As we saw in the first of the two parters, Celestia summoned one Dark Crystal, and it quickly brought forth more on its own. She quickly used her light magic to break them away, but had she left it alone the crystals might have run rampant on their own.

I also believe he can 'corrupt' normal crystals into his Dark Crystal. Just look at what he did when he returned to the Crystal Empire. The clear crystal houses transformed into his dark crystal huts. It's like his very presence corrupts everything around him.