I'll try to explain but I encourage others to reply as well.
broken spirit: Actually it's a term used when someone approaches God in a way in which they are vunerable and really seeking forgiveness for the sins thet have done and is required by God when you approach Him.
The sacrifices of God [are] a broken spirit: a broken and a contrite heart, O God, thou wilt not despise. Psalm 51:17
Evil spirit: a real spirit in which it's a demon, usually a general term for all demons
Familiar spirits: Types of demons in which is a resident to a place or a specific person telling that specific person what to do(wizards, witches, etc,)can be attributed to ghosts also.
Lev 20:27 A man also or woman that hath a familiar spirit, or that is a wizard, shall surely be put to death: they shall stone them with stones: their blood [shall be] upon them.
Free spirit: I think its the spirit of freedom from sin but I do not exactly.
Psa 51:12 Restore unto me the joy of thy salvation; and uphold me [with thy] free spirit.
Good spirit: A term used for blessing, a term for happiness
Neh 9:20 Thou gavest also thy good spirit to instruct them, and withheldest not thy manna from their mouth, and gavest them water for their thirst
Holy Spirit: The third part of the Holy Trinity(Father, Son, Holy Spirit)
Lying spirit: An evil spirit which causes/tempts someone to lie
2Ch 18:22 Now therefore, behold, the LORD hath put a lying spirit in the mouth of these thy prophets, and the LORD hath spoken evil against thee
Unclean spirit: Another term for evil spirit
Mar 7:25 For a [certain] woman, whose young daughter had an unclean spirit, heard of him, and came and fell at his feet:
Hope that helps