I would like to become a private therapist (psychological counseling,
not massage!) in Massachusetts who can
see people hourly and get paid for it ---- what is the minimum kind of degree
I need in order to legally be able to do that (besides going to
college of course)? I want to find the
cheapest, shortest degree that would allow me to do this. It doesn't
need to be prestigious degree or a fancy program, just enough to call
myself a therapist.

"...the following states do not have controlled titles for the term
'therapist' or 'counselor':

California, Florida, Hawaii, Iowa, Massachusetts, Minnesota, Nevada,
New Hampshire, New York, Rhode Island, Vermont, Virgin Islands"

http://www.m-a-h.net/hip/

Alrighty: I want to be able to get insurance reimbursement as a
therapist or mental health counselor. I think there's some degree
called LCSW or something? I think? I want to be able to have people's
insurance pay me, that way I'm a  "real therapist"

This may be helpful:

http://www.mass.gov/dpl/boards/sw/faq.htm

Unfortunately those social work degrees won't be of help to me --- I
am not getting my undergrad degree in sociology and I don't want to
waste two years getting a master's in social work (if I can avoid it).

I would like to know if there are any one-year or less-than-two-year
programs that certify one as a mental health counselor able to get
reimbursement from insurance. Perhaps that is only attainable with the
master's in social work? Not sure, the website doesn't seem to explain
that.

Health insurance policies vary widely in their coverage for
psychotherapy. Even a certified social worker with a Master's degree
may not be covered by some policies. A few policies won't cover any
therapist who is not an MD.