Yes, they are (mostly)
This is actually an interesting question. While things like Eagle Splendor clearly won't work on golems and most constructs (which lack an Int score), I don't think there is anything preventing constructs (in general) from being affected by mental spells or wearing magic items and benefitting from it.
Most of those spells, though, are subject to spell resistance, and many constructs are immune to spells like that. But there is no blanket protection on constructs as a creature type. So, while an Iron Golem cannot be affected by Owl's Wisdom even having a Wisdom score to be increased, due to their magic immunity, there is nothing preventing them from being affected by a Genius Avaricius (they have 1 charisma) and suddenly become more charismatic (as weird as that sounds). And is exactly how the game allows them to be targeted by Awaken Construct, and become an intelligent creature.
But, when dealing with constructs, you have rules all over the place. What would prevent your talking magic sword from having ioun stones orbiting her? Well, to activate an ioun stone you have to hold it, so that is impossible for our magic sword. Which equipment slots would be allowed is entirely GM Fiat, we don't have any rules for that.
So, if the magic intelligent item is created with the ability to cast Burst of Insight on itself (which costs an additional 1,200 gp), suddenly it can perform certain tasks much better than before.
However, there are many mental effects that still cannot affect a construct, even if they do have all 3 mental scores (like sleep), simply because they are immune to those effects by being constructs.
Immunity to all mind-affecting effects (charms, compulsions, morale effects, patterns, and phantasms).
Immunity to bleed, disease, death effects, necromancy effects, paralysis, poison, sleep effects, and stunning.
Not subject to ability damage, ability drain, fatigue, exhaustion, energy drain, or nonlethal damage.
Immunity to any effect that requires a Fortitude save (unless the effect also works on objects, or is harmless).
Constructs do not breathe, eat, or sleep.
They are immune to all these effects, regardless if intelligent or mindless. But keep in mind that magic items (intelligent or not) are never given Hit Die, so we can't tell for certain which effects should affect them as creatures or not. For instance, what would be the effects of Simulacrum or Reboot on an intelligent magic item?
All we know is that they take damage just as any other item and not as creatures:
Magic items, unless otherwise noted, take damage as nonmagical items of the same sort. A damaged magic item continues to function, but if it is destroyed, all its magical power is lost. Magic items that take damage in excess of half their total hit points, but not more than their total hit points, gain the broken condition, and might not function properly.
