Ioun Stone of Might

[Nezkrul]

+4 item bonus to strength-based skill checks and strength ability checks...

does that include strength attacks since those are basically strength checks?

[CM]

I don't have a reference to cite, but no. A strength attack is separate from an ability check or skill check.

[pemerton]

If a reference is needed (and it really shouldn't be!), here it is (PHB p 25):

The D&D game uses three basic kinds of checks, which are described further below: attack rolls, skill checks, and ability checks.

Hence, an item expressed as applying to skill and ability checks does not apply to attack rolls.