... it says used to be in the canon, and are still worthy of veneration. These were Joseph and Aseneth, Testament of the Twelve Prophets, The Martyrdom of Isaiah, The Epistles of Jesus Christ and Abgarus King of Edessa, The Third Epistle of St. Paul to the Corinthians, and the Acts of Paul and Thecla. My question is, when did the Armenian Church cease to include these books in the canon, and why does it still consider them worthy of veneration if they aren't worthy of canonization (assuming of course that the information I read is correct)?
That information is not completely correct. There could be and were canon lists that also included those above-mentioned books but they never became accepted canon lists for the Armenian Bible. One can see this, for example, in the canon list of St Gregory of Tathev, in which he doesn't mention those books of Asaneth etc at all (only the short testaments of the prophets are added to the main books of the prophets and the III epistle of St Paul to Corinthians).http://www.islamic-awareness.org/Bible/Text/Canon/armenian.html
I didn't have time to read myself what is written in the article you have mentioned, but if it really says that those books of Asanet etc "are still worthy of veneration", then this is completely untrue.
But I would add another apocryphal book of the New Testament which is not mentioned in that article but which should have been mentioned instead of all those books. It is the "Story of the Dormition of St John the Theologian".
This small story was part of the Armenian New Testament and it was frequently quoted in the writings of the Armenian Fathers. It was so popular that Nerses of Lambron wrote a commentary on it, commenting all the verses of that book, just like he would do it with other biblical books.