TL;DR: For the pillars: nephritic jade. Sounds good, looks good, is super tough. Better hope you don't have earthquakes though.
The ceiling is where you're gonna have real problems. A plain flat ceiling will collapse unless you use a roofing material with a really high tensile strength. You probably want to vault it, too.
Lets look at a single pillar first. Though you've defined pillar spacing, you haven't mentioned pillar layout so it isn't entirely clear quite what proportion of the surface world each pillar supports. Lets imagine that it is a cylinder a mile across, and a mile high. I'm going to move to using metric units now, because imperial ones are weird. With a volume of about 3.27 billion cubic metres, and assuming it has the same density of continental crust, it'll have a weight of about 9.26 billion tonnes. Assuming the pillars are perfectly cylindrical (you said they weren't, but didn't give a minimum diameter) their cross-sectional area will be 2.03 million square metres and therefore the pressure they'll be under will be about 178.65MPa (for reference, the compressive strength of concrete can be as high as 25.57MPa, so your pillars need to have stronger than that).
There's a frequently cited, but never actually referenced figure that suggests that the rock with the strongest compressive strength is nephritic jade at 400MPa. I'll take that figure as true, though it could be a load of cobblers for all I know (a figure cited here suggests more like 370MPa, but it is still just about high enough for our needs). It has a density around 3.15g/cm3. The weight of the pillar and the earth above it combined give a pressure at the foot of the column of 278MPa. Using nephritic jade would give you a safety margin of about 1.43. Note that this is a static safety margin... if your hollow world experiences earthquakes, you might have more serious problems, but that's a question for another day.
What I'm less sure about is the bulging of your pillars as they're squished from the top. I think they might be OK, but I'm quite far from certain on that. Maybe some nice metal reinforcing bands might help?
The next problem is the unsupported span of earth between two pillars... there's at least a half-mile gap between the edge of one pillar and the start of the next (I say at least, because depending on how your pillars are laid out the gaps might be larger... in a square grid, the diagonal spacing is more like .91 miles) and that's a big span for rock to cover. Even nephrite with its impressive compressive strength isn't nearly as strong in tension and has a tendency to fracture instead of yielding.
I threw some figures into the simple bending equation, and they didn't come out well. I'm not a structural engineer, so I won't repeat my amateur scribblings here because they're so far from an accurate assessment of the situation but: that roof ain't gonna hold, even if it were pure jade. The unsupported span is just too great. It'll crack in the middle, and everything will crash down into hell, crushing everything. Sure, the surface world will be ruined but hey! no hell anymore!
You might be able to fix this with a carefully vaulted ceiling, but I wouldn't want to say for sure. Really, you need to be making that ceiling out of some kind of reinforced composite if you don't want it to be crashing down on you.
