Death Prophet is a very strong midgame carry with great pushing, which fits her nicely into the current metagame. Her ultimate does absurd amounts of damage, the problem is that she's naturally a rather squishy hero and thus can't effectively stay alive long enough for it to deal damage. She's also rather level dependent and has no escape mechanism, making her in a solo mid role extremely vulnerable to ganks, especially in high tier play. I almost exclusively take her solo mid despite this, however, as she needs the levels and gains a lot of effectiveness from rune control. She's also not great in 1v2 lanes, even the safe lane.
Starting items: 3 branches, +3 INT, +2 all, and Tangos. Rush yourself a bottle and then Arcane Boots as soon as possible, finishing the Talisman and Magic Wand when available. An alternative start is 3 iron branches, 2x +3 STR, and Tangos, which will let you get a quick Urn. Usually there's a better wielder on your team as she's not a great ganker, but this item is stupidly powerful and every team should have one, so pick one up if you don't expect anyone else to.
Use your Wave at x:50 or so to push the lane and control runes- this makes your opponent have to choose between experience from your now advancing creep wave or contesting the rune. If it's invisibility or haste consider ganking; if it's regeneration or illusion use it to gain an advantage in your lane, and if it's DD you can do either. In lane, try to use her Wave to pick up multiple last hits and harass at the same time- the range is enormous but it must be cast carefully. Be very wary of missing opponents and ask for wards if you don't have them, her early game needs to be strong or you'll have a weak midgame.
From there you'll be working towards a Bloodstone, typically picking up the Point Booster and Vitality Booster first and disassembling your Arcane Boots to complete the Soul Booster, which gives great regeneration in and of itself. (I just learned this last trick recently so you won't see it in the replays below.) If you're farming extremely well and don't feel that you need the extra HP, you can pick up the Perseverance pieces first to improve your farming even more. Turn your now plain boots into Phase Boots at some point during this time, or if your team really needs it get another set of Arcane Boots.
When you've finished Bloodstone, you want other stuff that's going to keep you alive. Against heavy physical damage opponents go Blademail, Shivas, or Assault Curiass. Against a singular hard carry go Sheepstick, Cyclone, or Ghost Scepter. Against heavy magic damage opposition go Hood, Pipe, or Heart. Extremely rarely you can consider a BKB, but since her ultimate isn't too affected by disables unless it remains uncast you usually shouldn't worry about it.
Typical skillbuild: QEQWQRQEEERWWW+R ... this rarely changes, the only possible difference might be swapping Silence and E at level 2/4.
In teamfights, her ultimate needs to be used aggressively, because as you pointed out, they can just run away from it. If they chose to run away, you should be getting a free tower, so only ultimate when you need to- if the threat of your ultimate is making the team wary of defending the tower, take the tower for free and keep going. You should be coordinating with your team during midgame to push as soon as possible, usually taking all Tier 1 towers before 15 minutes. The range on her ultimate is huge, you need to be focusing your spirits to deal damage to buildings from afar. If they want to initiate on you, they should have to go through your team to do it. Choose a key target and right click them: your spirits will attack whatever you do. Don't undervalue her silence, at 6 seconds and with an extremely large AoE she's formidable as hell in teamfights. The later the game goes, however, the weaker she becomes. Like most midgame carries, her effectiveness compared to other heroes peaks at level 16, and so if the game lasts more than 40-45 minutes you had best not be the only carry on your team.
I'm 10-2 with this hero, here are some example MatchID's of my play:
- 9235655: A 1v2 safe lane for a change: 5 minute Arcane Boots, 18 minute Bloodstone, 27 minute Heart.
- 8749900: a coordinated push team with friends after we saw our opponents take far too many carries.
- 8366759: rather typical game showing how strong she is in lane, even against the highly-valued Rhasta.
- 3391570: just a complete stomp.
- 3053432: a game against a lot of good counters of Krobelus that borders on going too long.
Best Answer
The active effect of Phantom Assassin's Blur - that is, the invisibility even while attacking, using items, and under true sight - is dispelled 0.75 seconds after moving within 600 units of an enemy hero, not instantly. Since Phantom Assassin is invisible, Juggernaut's Omnislash can't find a valid target to continue attacking and ends.
Keep in mind that after the rework of Omnislash, the damage is no longer physical spell damage, but Juggernaut's autoattacks themselves. This means they can miss, and Monkey King Bar does not grant true strike anymore.