Naga is by my favorite hero in DOTA because of her ability to take on multiple heroes at once. Her illusions combined with diffusal blade and ensnare is one of hardest things to get away from in a chasing senario. The build that I use is more a personal preference and the later items might not follow the usual norms.
Level 1 : Mirror Image
Level 2 : Ensnare
Level 3 : Ensnare
Level 4 : Rip Tide
Level 5 : Ensnare
Level 6 : Song of the Siren
Level 7 : Rip Tide
Level 8 : Rip Tide
Level 9 : Rip Tide
Level 10: Ensnare
Level 11: Song of the Siren
Level 12: Mirror Image
Level 13: Mirror Image
Level 14: Mirror Image
Level 15: Stats
Level 16: Song of the Siren
Level 17-25: Stats
Mirror Image is leveled first to provide a way to disjoint spells like Sven's stun and is maxed until later because in the early game, if you actually max illusions, they don't deal that much damage and are very weak overall since siren is pretty squishy in the beginning of the game.
Ensnare is leveled to 3 as soon as possible, since 4 seconds is already a great duration and enough to get early kills. This is just a personal preference because I find using ensnare to gank is much more useful than to using rip tide for the damage and armor. However if your lane has enough disables to get kills then by all means max out Rip Tide, but generally I find ensnare much more useful for saving teammates and insuring kills (did I mention it goes through magic immunity).
Rip Tide is maxed out after ensnare because of the armor reduction and nuking damage. At this point of the game, you'll be doing enough damage so that the armor reduction will benefit you more than it will early game and with the extra levels of ensnare it makes it much easier to hit Rip Tide and get the couple auto attacks for the kill.
Song of the Siren is leveled at the usual 6, 11, and 16 and is used in many scenarios. I like to be aggressive with it and use it to set-up ganks, but it can be a very effective way to counter initiate the enemy team and provide a very good escape mechanism. The cool down is pretty long, so use it wisely
Strength - 21 + 2.3
Agility - 21 + 2.75
Intelligence - 18 + 1.95
Damage: 56 - 58
Attack Speed: 121 (1.40s per Attack)
Range: 128 ( Melee )
Tbe stats that stand out the most is the high base movement speed of 320 and all around decent attributes and attribute gain for an agility hero. This means that Naga isn't as squishy as most agility heroes and can last hit pretty effectively with base 56-58 attack damage along with an early Ring of Aquila. From experience, I find that naga can be pretty mana starved so the early Ring can be very beneficial for Naga's early mana regen.
From here we can assess that:
-Great Team fights
-Very high movement speed
-Great escape/initiation/counter initiation
-Dominates with items
-Great great great ensnare
-Some mana issues
-Very item and level dependent
-Illusions have high cooldown and fragile early on
-Can be difficult to master
Typically I go with starting item build #1 because it provides the much needed stats and regen for the early game and cost efficient for building into a Ring of Aquila and Wand later on. The #2 build is mainly for those that want an early vanguard with the stout shield and last hitting power in exchange for extra stats and regen. Typically I don't get an early vanguard because the farm I use to get the vanguard can be used for the more important diffusal blade. Plus vanguard is typically obtained because players need the extra survivablity when maxing out rip tide. The skill build mentioned in this guide will almost always provide naga the best escape because the illusions provide disjoints and confusion while the ensare usually traps the enemy heroes long enough for you to run away.
By this time Treads should be the next priority as it provides the attack speed and stats that naga and her illusions can benefit from. Phase isn't really needed because ensnare will usually trap the enemies long enough for most naga players to get the kill.
Diffusal Blade is the best item Naga can get in the middle game. The once weak illusions now have the ability to harass enemy heroes combining both physical and magical damage. Once a enemy hero gets ensnared, it's almost an ensured kill with a diffusal blade because even if ensnare runs out, there will still be an option to purge the escaping hero and get off those extra auto attacks. If naga manages to get diffusal really early, it's possible to harass the enemy heroes out of the lane while naga continues to farm for more great items.
I typically go Manta Style for the extra tank, movement speed, illusions, mana burn, and 1v5 potential. This makes it very difficult to focus on the real naga and almost always allows naga to successfully kill 1v2 situations because of the amount of damage all the illusions can do. After manta, a Daedalus is preferred since the critical chances apply to every single illusion you have, effectively amplifying naga's damage by that much more (it also replaces naga's long lost skill).
After Daedalus, if you haven't won already, it's most likely because of the fact that certain AOE skills are killing your illusions too quickly. This is actually why I get a Orchid Malevolence after all my damage items are complete. Orchid allows you to silence the most threatening AOE skills that can destroy naga's illusions which cuts Naga's dps potential. While silencing that hero, you have enough damage output to kill off the threats before finally finishing off the rest of the team. I get Heart because at this point, if you haven't won already, it't because of mana or damage, so its probably because of HP.
Get last hits and ensnare enemies that come close to towers or enemies that are being ganked for EZ kills. Use mirror image to disjoint certain spells if you're getting aggro'd or getting ganked and spread out the illusions to confuse the gankers. The purpose of illusions at this point are simply to get away from sticky situations. At this point, illusions do pitiful damage and take no effort to destroy. Your best bet is to try to confuse them.
If you have diffusal, get ready for some easy kills. As long as you cast illusions and ensnare the victim, you are almost certain to get atleast one kill. If the target still manages to tank the ensnare duration, diffuse them and auto attack them more to death. Setting up ganks should be a breeze as well since all you have to do is ult, walk into the enemy, and deactivate your ultimate when your teammates are there for easy kills. If you are getting group ganked, cast your ultimate and run away with your team mates or tp out AFTER your team does, to ensure everyone gets away.
At this point, if you have the late game items such as manta and daedalus, 1v2 are basically easy fights for you and tower pushing should only take a few seconds. If a naga gets this farmed, theres not much the enemy team can do to win, other than AOE skills. AOE skills are by far naga's biggest threats, so in team fights, always take out the AOE stunners and disablers.
Your friends include heroes that...well...can disable, especially silence. But more importantly heroes that have multiple stuns and disables. This is because naga is very good at taking out one hero very fast and switch to the next target immediately after. If she gets disabled taking out the first target, chances are she won't be able to get the kill after that.
: Shadow Shaman's Shackles is one of the longest disables in the game. Not only that, but he has a second disable Hex that is still are pretty long disable.
: If they can't disable naga, naga wins games.
: While not much of a support, he can silence one hero while slowing another one. This makes it so that naga can finish off the silenced hero before aiming for the slowed one.
: Two longest disables, nuff said
: Because repel is too good to not mention
Enemies of naga are AOE casters, especially the ones that can disable. They ruin illusions and therefore destroy naga's damage capabilities making her less effective during the game.
: Enigma's ultimate is just too good on Naga. With a blink dagger, enigma basically makes naga useless during team fights.
: The burst damage on his ultimate as well as the follow up stuns will destroy your chances of even touching someone on the enemy team.
: His ultimate kills anyone with illusions in general.
: If he gets off a good ultimate, he can kills your illusions while probably out dps you with insane amounts of auto attack damage
: His ultimate literally ravages your illusions and its basically impossible to avoid, especially if he gets a blink dagger.