Psalms: obviously referring to the book of Davidic psalms, essentially the hymnal of the Jewish nation, the singing of which continued (and continues) to be enjoyed by Christians.
Hymns: Hymns were originally short poems or songs of praise to a deity or deities. The early Christians adopted the form for worshipping the true God.
Spiritual songs: "Songs" (literally "odes") seems to be a general term for other kinds of verse intended to be sung. The songs used in corporate worship ought to be limited to spiritual matters, but the term does seem to permit some liberty to sing of things other than direct praise of God--encouragement, exhortation, and so forth.
So suitable songs for corporate worship are those that are Scripture set to music, which glorify God and edify the saints.
As to "style," if the title of the thread is inquiring about musical genre, Eph. 5:19 (and Scripture as a whole) is silent. I think we can infer that if the early Christians adapted hymnody for their own use, they probably brought a few familiar tunes with it--which suggests that we needn't fear the use of contemporary musical genres in our own worship, either.
I'd say some genres have a disconnect between form and function (e.g. louder, more aggressive musical forms like heavy metal and its infinite variants), which would make them inappropriate for corporate worship, and better off listened to at home instead.