When there is an invisible enemy on the battlefield, does the owner of the weapon see the enemy? Or would the weapon tell the owner where exactly to strike although the owner only sees empty space?
Depending upon the effect, an intelligent item may be able grant the effect to its possessor, but, like an NPC, the intelligent item's not obligated to
Intelligent items have their own independent action economies, desires, and wills. Although an intelligent item will frequently use its powers on behalf of and at the behest of its owner, it can sometimes refuse.
Intelligent Items on Intelligent Item Powers says
Each intelligent item should possess at least one power, although more powerful items might possess a host of powers. [...] All powers function at the direction of the item, although intelligent items generally follow the wishes of their owner. Activating a power or concentrating on an active one is a standard action the item takes. The caster level for these effects is equal to the item's caster level. Save DCs are based off the item's highest mental ability score.
Emphasis mine. This means, for example, that Snakebite, an intelligent item with the special ability true seeing at will, can, on its turn, take a standard action of its own to activate an effect like the spell true seeing on itself. Snakebite can then communicate what it sees because of that effect to its wielder via its telepathy. This has no more (and no less) game effect than if another creature communicates to the wielder what it sees.
Also, Snakebite possibly could, as this answer mentions, use the true seeing effect on its wielder, too, as true seeing has a Target entry of creature touched, if the GM determines that a creature touching Snakebite is the same as the sword being able to touch the creature. (That is, the effect's creator "must be able to see or touch the target," and while the sword can be touched to others, the GM must determine if this is the same as the sword being able to touch the target, lack of independent motion notwithstanding. Seriously, I think (hope!) most GMs would view a wielder touching another or himself with the sword as equivalent to the sword itself doing the touching, but it's wise to ask.)
Likewise, effects duplicating spells having entries of Range: Personal, Target: You, or both should, unless the GM rules otherwise, only affect the intelligent item rather than the wielder, sometimes with odd results (e.g. blink, mirror image) (This GM urges others not to distribute intelligent items with such special abilities unless the GM wants baffled players.)
However, Snakebite's special ability true seeing is a dedicated power, and dedicated powers are more restricted. Intelligent Items on Dedicated Powers says
A dedicated power operates only when an intelligent item is in pursuit of its special purpose. This determination is always made by the item. It should always be easy and straightforward to see how the ends justify the means. Unlike its other powers, an intelligent item can refuse to use its dedicated powers even if the owner is dominant (see Items Against Characters). The caster level for these effects is equal to the item's caster level. Save DCs are based on the item's highest mental ability score. See Table: Special Purpose Item Dedicated Powers for a list of dedicated powers.
So unless the wielder convinces Snakebite that there might be a serpentfolk under the effect of an invisibility spell Right now! Over there! it can refuse to use the true seeing at the wielder's command. (Were I GMing, I'd have Snakebite using its true seeing ability all the time but have the weapon relay only evidence relevant to serpentfolk without prompting, but I would also have Snakebite make Perry the Platypus noises yet call them mongoose noises. I expect your GM will vary?)
Before introducing intelligent items into the campaign I recommend that the GM make sure he's familiar with the host of rules associated with intelligent items. Adding an intelligent item to the campaign adds another NPC to the campaign world, and the GM must be prepared to play that often single-minded, emotionally stunted, and relentlessly demanding character.
If the item were using its own senses and telepathically relaying information, then: The item would tell the owner the location of invisible enemies, thus allowing the owner to attack the right square, but still subject to a 50% miss chance. The item would tell the owner about illusions it has identified, thus giving the owner +4 on Will saves to disbelieve.
However, true seeing has "range: touch", not "range: personal".
This means that an intelligent item or creature that has a spell-like ability of true seeing at will is not limited to enhancing its own senses: it can also give enhanced senses to its allies. If you are actively pursuing the item's agenda and thus convince it to use its dedicated power at all (see @HeyICanChan's answer for caveats about that), then your whole party can have true seeing. So you and your allies directly see invisible enemies etc, but only in certain circumstances.