As far as I understand, a neurosis is any abberation from normal. As Earnshaw said, they can be very mild and are often just a personality quirk, although they can be damaging to the person who has them, I don't think they are generally damaging to others.
Okay, here's Wiki:
Neurosis, also known as psychoneurosis or neurotic disorder, is a "catch all" term that refers to any mental imbalance that causes distress, but, unlike a psychosis or some personality disorders, does not prevent rational thought or an individual's ability to function in daily life. It is particularly associated with the discipline/school of psychoanalysis, which is not to be confused with psychology or psychiatry.
Psychosis, according to Wikipedia:
Psychosis is a generic psychiatric term for a mental state in which thought and perception are severely impaired. Persons experiencing a psychotic episode may experience hallucinations, hold delusional beliefs (e.g., grandiose or paranoid delusions), demonstrate personality changes and exhibit disorganized thinking (see thought disorder). This is often accompanied by lack of insight into the unusual or bizarre nature of such behaviour, difficulties with social interaction and impairments in carrying out the activities of daily living. A psychotic episode is often described as involving a "loss of contact with reality". The American Heritage Stedman's Medical Dictionary defines psychosis as "A severe mental disorder, with or without organic damage, characterized by derangement of personality and loss of contact with reality and causing deterioration of normal social functioning."
And weird means something different every time depending on who's calling whom weird.
