The St. Vincent invoked is St. Vincent of Saragossa (i.e., "St. Vincent the Deacon"). The St. Anthony invoked is not St. Anthony of Padua, but St. Anthony of the Desert -- the Father of Monasticism. The St. Catherine invoked is not St. Catherine of Siena, but St. Catherine of Alexandria. The John and Paul invoked in the martyrs section are two pre-congregation martyrs, both of whom are also invoked during the Communicantes of the Canon of the Mass.
In the Latin version, you'll note that the section in which the Saints are invoked has two options for the response: "Ora pro nobis" and "Orate pro nobis." The first is used in response to the invocation of a single Saint; the latter is used in response to the invocation of more than one Saint. This is because Latin verbs are conjugated differently in the second person depending on whether the subject addressed is a single individual or more than one person.
The Litany of the Saints -- the oldest of the litanies, dating to A.D. 595 -- is prayed liturgically at the Easter Vigil, during ordinations, on Rogation days, and also during solemn exorcisms, etc.. Privately, it is prayed any time one wishes, as with the other litanies, but is especially prayed after sundown on All Saints' Day in preparation for All Souls' Day, and on All Souls' Day itself.
This litany first invokes God in all Three Persons, then follow, in this order: Mary; the blessed spirits; St. Joseph and the Patriarchs and Prophets; the Apostles and Evangelists; all the disciples of the Lord; the Holy Innocents and the glorious martyrs; the holy Bishops and Confessors (those who suffer for the faith); the holy priests and Levites; the virgins and widows; and all holy men and women.