If you're having trouble rooting an enemy with Nevermove, try throwing it at opponents when they are near their minions so the explosion surprises them.
While laning, try to use Death's Hand's piercing damage to damage opponents from a safe distance.
Vision of Empire is quite difficult to land on its own, look for skirmishes around the map where enemies may be distracted or crowd controlled so you can land it more easily.
Demonic Ascension may make Swain very hard to kill but he's pretty easy to get away from. Try building items that can slow opponents to keep them in range if their mobility is overwhelming.
Swain's passive is very potent if you are immobilized. Make sure to be extra careful around enemies who have immobilizing effects.
High mobility counters all of Swain's basic abilities: Death's Hand does more damage the closer he is, Vision of Empire has a very long delay and Nevermove must start returning back to him to be dangerous.
Buying an item with Grievous Wounds will make Swain much easier to kill during his Demonic Ascension.