Atheist: I do not believe there is a god. This can also mean I do not believe in god.

Agnostic: without Knowledge, depending on very loose definitions on can not say that a god that by definition can not be perceived can not exist by definition.

Spiritual: anything and everything. The important thing here is if you say spiritual it will be misunderstood by the person hearing. This is believing that the metaphysical exist. By definition if it does not exist in the physical world it does not exist. the metaphysical is defined as that which exist outside of the physical and thus, by definition does not exist.

Theist/Atheist: Those that are convinced or unconvinced in the existence of a God(s)
Agnostic: Those who are uncertain to the existence/nonexistence of a God
(Non)Spiritual: Someone who has some sort of innately spiritual belief such as the existence of a Soul.

You can be one, or all of the above, but you can't be a Theist and an Atheist at the same time, naturally. You can be an Agnostic Theist, someone who is unsure as the the existence of a God but still believes there is despite this uncertainty. An Agnostic Atheist, someone who is unsure to the existence of a God and, usually due to that, does not believe there is one. A Spiritual Agnostic Atheist, someone who fulfills the above criteria but is also convinced to the existence of Angels and Demons, just as an example. This is not a comprehensive list of examples and more variables exist, such as what could be referred to as a Gnostic (not the Christian denomination) someone who is convinced of the existence or at least the possibility or probability of the existence of a God(s).

Atheist - Nothing supernatural at all.
Agnostic - Will believe in supernatural beings or "power" if evidence is provided.
Spiritual - A belief in a connection between other people an/or other living things. The connection can be super natural or instinctual. So, if instinctually based belief, even an atheist can be spiritual.

I do not see instincts as "supernatural" but rather are hard wired into (most of) us for better survival, and often use unconscious cues, which may or can appear to be supernatural at times, but can be logically explained once they are understood.

An atheist declares any suggestion of the divine or supernatural preposterous, whilst an agnostic recognizes their own falsifiable hypothesis regarding any (untestable) postulate and the spiritual wilfully accept the existence of systems which cannot, presently be subjected to scientific method. Neither atheists nor spiritualists observe scientific method, its very first rule is a falsifiable hypothesis.