Someone or something that is eminent is of high rank, noteworthy, distinguished, or prominent. An accomplished world leader and a respected intellectual, for instance, are eminent.
Something that is imminent is (1) very near or (2) impending. For example, when the weather forecast calls for a 100% chance of thunderstorms, we might say that storms are imminent.
Something that is immanent exists within or is inherent to something else. The word is often used in reference to spiritual or otherwise nonmaterial things. For example, a spiritual person might say that God’s power is immanent to the natural world.
Though the three adjectives are not exact homophones, they are similar enough to engender occasional confusion. Immanent in particular is very often used in place of imminent in popular usage, and imminent and eminent are also frequently mixed up.
For the first time this year, balloters must weigh the fate of two eminent stars, Barry Bonds and Roger Clemens. [New York Times]
Even under these limitations it is only 4 to 1, on the average, against each child of an eminent son of a judge becoming a distinguished man. [Hereditary Genius, Francis Galton]
We, as thinking-acting-being students of liberal arts, must reconcile some things immanent to our existence. [The Occidental Weekly (link now dead)]
The Diaoyu islands, including its affiliated islands, have been China’s immanent territory since ancient times, and China enjoys indisputable sovereignty over these islands. [People's Daily]
The authorities have studied all the available intelligence and “the conclusion overall is that there’s no concrete evidence of imminent attacks in Germany.” [Bloomberg]
WSJ: Blockbuster Bankruptcy Filing Imminent [Headline, Home Media Magazine]