None. Colloquially, we use "hole" in all kinds of weird ways. As others have pointed out, topologically a straw is no different to a torus (donut) that clearly has one "hole"... but I'd like to focus instead on the linguistic definition of "hole", not the colloquial or mathematic definitions.

A hole can either mean:

1. a perforation ("a hole in my shirt", "a bullet hole", etc) - which is, specifically, "a hole or pattern made by or as if by piercing or boring"
2. a gap ("a hole in your reasoning", "a hole in my heart", etc)
3. a hollowed out or burrowed place ("a hole in the road", "a fox hole", etc)

i think we're not talking about 2. It seems to require some larger uniform structure or set of items in which an item is missing. 1 and 3 seem really similar to me: both seem to require some active removal of matter to qualify. All of these definitions point towards a subtractive process, where something of a larger whole (heh) is removed or absent.

Most straws, I'll venture a guess, are not manufactured solid and then bored out.. so I don't think it applies here. So I don't think a straw matches a fitting definition of "hole". A straw is created additively by assembling the "shell" by some means, not subtractively. Donuts, by comparison, had holes punched in them. A subtractive operation. Rubber bands have not had holes punched in them... they're additive. Not holes.

Similarly (because I see a lot of talk about buttholes and mouths here too), your esophagus and digestive tract (and veins and all kinds of other things) were formed in a similar additive manner, not by forming a mass of meat and boring through the passage, and thus would similarly not qualify as "holes" (in my opinion).

By the logic of most of the comments in here, does this mean most people are wrong when they say they are digging a hole???

Judging by what this video by Vsauce about how many holes a human has it should be one in a straw. A straw is basically just a long doughnut and there's one hole in those.

Well, depends what you call a hole. Does a glass have a hole? Does a bottle have a hole?

If you said no to both, you mean a topological hole and a straw has one.

If you said yes to one or both of them, you mean a tight opening in which someting can be inserted (yes yes, innuendo). How tight an opening must be to be a hole is arbitrary and subjective, it depends on the person. In this case a straw has two holes.