Spirit Walk is actually pretty straightfoward after a couple of uses. For the duration of the spell (2-3 seconds) you are able to move through any enemies, and remove all movement impairing effects.
This means:
Slow down effects are removed.
You can escape most roots, such as from any Jailer type elites.
You can walk through enemies (if you can click a free floor space).
You cannot walk through anything physical however. Any effects which create a game-object "cage" will trap you... ie Diablo's cage spell.
You cannot walk through the walls created by "Waller" elites.
You cannot walk through closed doors.
You cannot walk through walls.
I just ran a few tests because I was curious on this and wanted to know myself since I'm maining a Witch Doctor. My findings are as follows.
Testing Method: I used the abilities on a monster (or multiple) and watched damage against them. I removed gear and equipped it while DoTs were ticking on targets, and I also used INT Boost abilities while DoT effects were ticking on targets. To test Spiders I did something similar but had to time it better. I also had no runes active and no passives active. I didn't try to get screenshots, but if you'd like me to redo the test and try to get good screenshots let me know and I'll edit them in.
Scenario 1: Grasp of the Dead - Gaining INT while Grasp of the Dead is already on the ground does not appear to effect Grasp of the Dead's damage. Damage is calculated when spell is cast and damage dealt doesn't appear to change when INT is increased post cast.
Scenario 2: Corpse Spiders (already thrown) - Gaining INT while Spiders are already on the ground does not appear to effect Corpse Spiders' Damage. This was also true for Tiki Men.
Scenario 3: Haunt and Locust Swarm - Gaining INT while Haunt and Locust Swarm are already on a target does not appear to effect Haunt and Locust Swarm's Damage. Additionally, the damage of Locust Swarm bounces ALSO does NOT appear to be effect by INT gains.
Scenario 4: Summoned Pets/Minions - As far as damage is concerned: Damage is calculated for Gargantuan ON HIT. Meaning when he swings at a mob your stats at that moment are the deciding factor on how much he hits. This was also true for Zombie Dogs. I was not able to test if and how INT effects their other stats because I don't know a way to display that information for summoned minions.
Additionally, I also tested if weapon damage being applied changes the situations and all of the above scenarios are still true.
These tests show the following:
1) Damage calculation for persistent effects (DoTs, AoE Damage Pools, Non-Minion Summoned Creatures, and etc) is calculated as soon as the spell is cast and damage is not retroactively applied when the player's stats increase.
2) Damage calculations for minions (Gragantuan and Zombie Dogs) is calculated when that minion hits a creature, thus will gain bonuses for increased INT.
These were all tested on a level 60 Witch Doctor so I can't say if they apply to all classes, but I can probably safely assume they do. I also didn't test how damage is calculated for hired mercenaries, but from the test we can also probably assume it is on hit.
An easy way to test this yourself would be to go into Act 1 of any difficulty (I suggest the highest you can go). Then go outside the first area with INT items unequiped and use abilities on the zombies in that area and then equip them mid fight, and hitting enemies with abilities like Soul Harvest and looking at the damage increase. You can display your damage dealt to enemy creatures by going to Options -> Gameplay -> and Checking "Display Damage Numbers"
Best Answer
Spirit Walk renders you invisible for the duration, although your "old" body stays where it was, and monsters can continue to attack it. If your "old" body suffers damage equal to 50% of your life, the spell ends early.
In addition to the invisibility, run speed increase, and the ability to walk through monsters, it breaks every and all effects that restrict movement.
It removes snares, stuns, jail effects, freeze effects, and any other effect, while making you immune for the duration (walls, however, still block you).
New monsters will "ignore you" if you pass by them, but are out of sight before the effects of the spell wear off. In other words, you do not aggro new monsters while spirit walking (although your follower or minions following behind could, if they don't wind up warping past the monsters to catch up with your increased speed).
One other undocumented effect is that you no longer take any damage while the spell is active, so you can safely walk through area effect spells (such as the effects of bosses such as Belial and Azmodan). Damage to your body after you leave it with this spell does not effect your overall health; it merely has the potential to end the effect early. If you are surrounded, are taking damage, and use Spirit Walk at 1% health, then the monsters continue to attack your body but do not hurt you. If the continued attacks would do damage equal to 50% of your health after you cast the spell, then the spell ends, but you are no worse for wear than the moment you activated the spell.
As an example, I used this spell repeatedly on Belial. If I was too close to one of the green pools indicating that he's going to take a swing at me, I'd pop Spirit Walk. His attack would hit my body, ending the Spirit Walk early, but I would take no damage from the attack.
Another major, major benefit to this spell is that you can pick up health globes while under its effects. This means that you can safely run through champion packs, rares, and uniques/bosses while low on health to snag some much-needed healing that would otherwise be far too dangerous to pick up (e.g. in the middle of multiple arcane lazers, molten magma trails, etc.).