The body is descibed in scripture as a tent or tabernacle. Jesus, when speaking about the new eternal body, referred to it as being a "mansion" that He went to prepare, and it is also known as a temple of permanence once it has been filled with a spirit.
The soul is the mind of man - the sentient being that is self aware and living, yet incomplete; not having the spirit that connects it to God who is a spirit. I know that sounds contradictory, but even though God is a spirit, He is also not limited in His ability to manifest Himself in other forms. He is All in all, as in the verse that says poetically that "we live and have our being" inside of God or the fact that Jesus is God manifested in the flesh. Each is seperate in person, but one as God.
Most of Christianity speaks of the triune God, Father, Son, and Holy Spirit, and there is a large concensus that also hold to man as being triune in nature at the begining when first created by God, but losing the spirit to death after disobeying God's warning of the death that came with sin.