The Phantom Stranger is a mysterious figure in the history of the world. His origins, nature, even his name, have never been revealed. Various stories about his origins exist, including:
Yet another adventure, Conjurors, has him as the Father of Magic, the first human ever to wield arcane forces through his medallion stolen from extra-dimensionnal Lovecraftian-type deities, arcane forces he then shares with humanity.
In his earliest appearances, the Phantom Stranger would prove supernatural events to be hoaxes. In later adventures, the supernatural events were real and the Phantom Stranger was given unspecified superhuman powers to defeat them. He later appeared in various other adventures, sometimes as a major participant; in others, the Phantom Stranger just appears and gives advice or warning to the featured heroes. Occasionally he serves simply as narrator. In some stories, he seems to be answerable to a mysterious Voice, implied to be God. 
The Phantom Stranger played a major part in The Books of Magic, taking protagonist Tim Hunter through time to show him the history and nature of magic. He has assisted the Justice League on numerous occasions, even being formally elected to the group.  The Stranger also tried to foil Eclipso's plan to cause a nuclear war.
He also attempted to prevent Hal Jordan from uniting the resurrected body of Oliver Queen with his soul in Heaven. This earned him Jordan's wrath; indeed, the Spectre threatened to judge the Stranger to see whether God had "punished" him properly by refusing him access to Heaven itself. Nonetheless, the Phantom Stranger has assisted Hal Jordan during his tenure as the Spectre on numerous occasions as well, most notably in a short stint babysitting Hal's niece, Helen.
During Day of Vengeance, the Stranger had been turned into a small rodent by the Spectre. He was still able to advise the Detective Chimp, who sheltered him in his hat while he recovered his powers. He changed back using recovered energies  and aided the Shadowpact, allowing them to see the battle between the Spectre and Shazam. That makes a point that the supernatural community generally regards the Phantom Stranger as invincible. The first reaction of some people to the Spectre's assault on magic is simply to presume that the Stranger will take care of it. Other adventures have shown the Stranger nearly as powerful as the Spectre. This however, is a recent interpretation. While others have never considered the Stranger as an easy foe to combat, given his unknown abilities, they also never considered him as invincible.
The Phantom Stranger's relationships with the other mystic heroes are usually a bit tense. The Stranger has no qualms gathering various forces in order to combat a certain evil (the Sentinels of Magic, but also other loose outfits), often invading those people's personal lives. However, he does not usually extend them that same courtesy. The Phantom Stranger has resisted such people as Doctor Fate (notably Hector Hall) in this, although Fate is in almost any incarnation an ally of the Stranger. Despite this, he does get along well with Zatanna; he appeared by her side to help remove the influence of Faust on Red Tornado. 
Since he is ultimately an unpredictable force, others often meet the Phantom Stranger's appearance with distrust. Nonetheless, most heroes will follow him, seeing not only his immense power, but also knowing that the Stranger is in the end, a force for good. Notable though is Madame Xanadu, who has refused to join the Stranger on a few occasions, although she is a member of his Sentinels of Magic.The Stranger also holds a unique relationship with the Spectre, as the two forces often come into conflict. He was responsible for gathering a group of mystic heroes in order to combat the Spectre, when its human host Jim Corrigan seemingly lost control of the Spectre. (It was during this time that they destroyed the country of Vlatava.) The Phantom Stranger participated in Jim Corrigan's funeral, when Corrigan's soul finally earned its rest and left the Spectre. The Stranger subsequently became one of the forces that stood against the Spectre when it went on a rampage without its human host, until the soul of Hal Jordan bonded with it. The Stranger occasionally took on an advisory role for this new Spectre. Aware that the Spectre now has yet another new host, the Phantom Stranger gathered a large group of magic wielders in an unsuccessful attempt to solicit the Spectre's assistance in the Crisis.
The nature of these are as mysterious as the man himself. The Phantom Stranger has demonstrated enormous powers and capabilities, the exact origin of which is undetermined.
Inter-dimensional Teleportation: He can travel at will among the magical dimensions, including the Realm of the Just Dead, the Antechamber of Souls (which may be another name for or a particular area of the Realm of the Just Dead), Heaven, Hell, Apokolips and the realm occupied by the Quintessence.
Mental Awareness: He has at least some telepathic abilities, and can ordinarily perceive truth and deception, good and evil.
Spectral Sight: He can see spiritual entities and travelers invisible to normal sight; he can perceive magical events at a great distance.
Teleportation: He can mysteriously vanish and appear at will, suggesting magical teleportation (when the JLA had a satellite in orbit 22,300 miles above Earth, the Stranger routinely entered and left it without use of the JLA teleportation tubes).
Oneiromancy: He can send dreams of omen, warning, or information, though possibly only with the permission of Dream of the Endless.
Dispel: He can dispel magic and sorcery, especially magic of mental control or illusion and deception.
Illusion Casting: he can also cast illusions and mind controls of his own.
Transmutation: He can perform some feats of transmutation, such as turning fired bullets into flowers and sticks into snakes and back.
Space Adaptation: He can survive and even communicate in outer space, though he may not be able to travel of his own volition while there.
Simple Sorcery: The Stranger almost never uses spoken spells, magical artifacts, or magical rituals more complex than a seance or a circle of entrapment.
Energy Blasts: He can fire energy bolts of great force.
Knowledgeable: He claims that "nothing remains hidden to him."Good Combatant: He is a moderately skilled hand-to-hand combatant, often surprising with a punch someone who smugly thought their protection against magic rendered them untouchable.
Flight: He does not fly in the material world.
Future Restriction: He cannot travel to the future.
Non-Direct Interaction: The Stranger's most important weakness, if that is what it is, is the sharp limitation on his acting directly and overtly. Threats which he would presumably have the raw power to directly defeat he must instead warn others about, especially if those others have some particular responsibility at stake. Even his information he apparently cannot provide clearly and explicitly; in many cases his warnings or clues are cryptic. It might be, for example, that he is forbidden from removing the responsibility from humanity's shoulders; he definitely believes in free will, and the availability of a balance of choices to humans. (The very entertaining free will debate in the Books of Magic was in fact perfectly in character for the Stranger.)
Magical Downside: The Stranger is not physically invulnerable. Especially when he is heavily outnumbered when his magical abilities are already in use, or when he is taken by surprise, he can be injured or knocked out. He can be imprisoned by magical means; and his innate magical energies can be siphoned away. His physical form can be destroyed and he can die in at least some circumstances. He has often thought that a particular combination of threats might destroy him, particularly those which combined magical imprisonment with physical attacks or magical drains. It may be that the Stranger is mistaken and that there is nothing which could permanently destroy him (nothing has yet, obviously); but he definitely believes that there are things which can.
Talkative: A weakness of a different sort is his oft-noticed tendency to speak too much; but this may be related to his need to make those around him understand the consequences of their choices and the fact that they face choices. He must not act in their place, so he must make them understand what their actions mean.