These two terms are often used very loosely, generally in a pejorative way. They actually have very specific meanings in religion and philosophy [see below]. In the popular sense, usually wrong, they refer to things mysterious, strange, bizarre, weird, and potentially harmful. In addition, the term "immanent", helpful in describing these words, is so philosophically technical, that it is often not found in simple dictionaries.

In my understanding, that which is "mystical" is directly perceivable, experienceable, and immanent. It happens through the use of all of our senses and reason, when taken together. It is the direct perception of the universal energy in daily life, as well as my participation in that energy.

That which is "occult" is hidden from common view and experience, usually by human choice. Often it refers to things which take special training and/or preparation to become aware of. I use this word to refer only to particularly difficult perceptions which require training to use. "The Occult" is a different matter, and refers to those esoteric practices which in the West are generally referred to as "magic" or "magick".

Neither meaning necessarily refers to a religious experience, though it may. Both refer to human experiences which are difficult to communicate in daily language, but so are the experiences of quantum physics and human psychology. In my pages, I try to use these words with the meanings indicated above.

From The American Heritage Dictionary:

mys·ti·cal (mĭs'tĭ-kəl) adj.
1 - Of or having a spiritual reality or import not apparent to the intelligence or senses.
2 - Of, relating to, or stemming from direct communion with ultimate reality or God: a mystical religion.
3 - Enigmatic; obscure: mystical theories about the securities market.
4- Of or relating to mystic rites or practices.
5 - Unintelligible; cryptic.

More at: http://en.wikipedia.org/wiki/Mystical

oc·cult (ə-kŭlt', ŏk'ŭlt') adj.
1 - Of, relating to, or dealing with supernatural influences, agencies, or phenomena.
2 - Beyond the realm of human comprehension; inscrutable.
3 - Available only to the initiate; secret: occult lore. See synonyms at mysterious.
4 - Hidden from view; concealed.
5 - Medicine. Detectable only by microscopic examination or chemical analysis, as a minute blood sample.
6 - Not accompanied by readily detectable signs or symptoms: occult carcinoma.

 More at:  http://en.wikipedia.org/wiki/Occult

im·ma·nent (ĭm'ə-nənt) adj.
1 - Existing or remaining within; inherent: believed in a God immanent in humans.
2 - Restricted entirely to the mind; subjective.