Nature - Certain innate personal qualities, perhaps acquired by accident of heredity, or maybe considered an expression of one's "nature," "essence," or "soul." These can only be sensed indirectly, they are hopelessly ineffable,
but permanent across lifespan AFAIK.
Character - Systemically rooted emotional outlooks induced during early critical formative stages of existence that go on to silently comprise the ulterior foundation of a person's values, ethics, principles, and beliefs in life—whether they know it or not.
Personality (not Socionics) - Conditioned imprints and behavioral strategies forged through collisions with familial upbringing and social enculturation. A series of interactions that ultimately converges into parameters defining one's self-esteem, personal hobbies/interests, and resultant persona. Greater malleability and potential for self-change exists here, however.
Disposition - The "long term moods" that set an overarching tone/color/theme on a person's experiential awareness. Can be negative or positive, generally induced by either prolonged stress or prolonged satisfaction. One may not always be acutely conscious of its influence upon them; mindfulness can render it a useful barometer of conscience for gauging whether one is making good/bad key decisions in life.
Mood - The generally transient ups and downs that occur in response to localized and immediate situations and circumstances. AKA, the stuff
gets accused of tinkering w/ the most. Self-explanatory I think.
Mental State - That which is contending with the exigent information processing demands of the moment. A dynamical cognitive portrait continuously emerging from the composition of one's current thoughts, impressions, reactions, objects of attention, focal priorities, and active motives.