Phoenix can play any role except lategame Hard Carry and is extremely flexible. Best as an Offlaner, Roamer (lvl 3), or Support. Mid is good in some matchups as you can control runes very easily and deny last hits with spirits.

Sap XP till level 3 and use spirits to slow attacks and deny creeps while they swing like a sloth. Typically best in counter initation scenarios to turn a fight and team wipe or to finish fleeing enemy. Sun ray can provide team sustain for multiple tower pushes. Ult (Egg) whenever you are running low on health or need to refresh your abilities and distract/dmg the enemy team. Remember to sun ray during ults if you have the talent.

Best Against: Slow right clickers (to survive egg and possibly aghs a teammate) or Lockdown like Chronosphere or Legion Dual due to spirit attack slow and sun ray dmg.
Best With: A tank with a stun or aoe lockdown that can benefit from sun ray heals and help keep egg alive or take advantage of the distraction.
Worst Against: Butterfly/BKB heroes with gap-close or extra range, Ursa, Lifestealer (built in magic immunity), sniper, etc. Instant stun supports (hex ...) can also be dangerous for offensive icarus dive use. Snapfire, Ursa, and Troll can counter egg. Silence is also hard to deal with (build a bkb).

Shard/Aghs/refresher Sup Phoenix is an option vs teams that may not be able to kill egg. Aether lens may be very helpful to pull this off. Remember not to pass up a good aggressive egg while waiting for a defensive egg. Aghs requires a double click to activate egg if you aren't bringing another hero in.

Tank phoenix is an option vs high dmg opponents with few stuns. You'll need armor, HP, and Blademail.