St. Luke was declared a saint before the official canonization
process was instituted in the 12th century. He would have been declared a
saint to the bishop by those who knew him best and were familiar with his
life and merits. The local bishop would them make the decision. Today
only the pope can declare saints after years of study by the Sacred
Congregation for the Causes of Saints in the Vatican. The church does not
create saints. Only God can do that. The Church "screens" candidates for
sainthood to determine if they had a life worthy of emmulation. In other
words, do they make good role models. Also, the Church has to be assured
that the person is actually in Heaven. That is the reason that today a
number of miracles must be verified before a person can be declared a
saint.
St. Francis Xavier was canonized with fellow missionary St. Ignatius in 1622.
St. Eligius was canonized in the Pre-Congregation era. This was when people were often canonized because of their popularity while they were alive.
St. Etheldreda was canonized by Pope Celestine III in 1198.
St. Anselm was canonized in 1494.
There are thousands of canonized saints, not just five.
St. Luke is a "pre-congregational" saint. In other words, he would have been proclaimed a saint by popular acclamation and devotion long before there was an established process within the Church for canonization.
No, Saint Patrick was never formally canonized
Yes, St. Odilia was canonized. She is known as a patron saint of the blind and visual difficulties.
St. Clare of Assisi was canonized on September 26, 1255, by Pope Alexander IV.
Catherine was canonized in July of 1461 by Pope Pius II.
Juan Diego was canonized on July 31, 2002.
Maria Goretti was canonized by Pope Pius XII.