To this day, readings from these books are not read in Syriac Churches.
(Only exception is the autocephelous Malankara (Indian) Orthoxox Syrian Church, which included some readings from these books in the late 1980s.)
I've never heard of Revelation being read in the liturgy (the few times it is listed in the Lectionary, it is presented as an option and, in practice I've never seen it read), but yes, pericopes from at least some of the other letters (II Peter, II and III John, and Jude) are read in the liturgy at certain points in the year.
The "lectionary reform" is of particular interest to me because the only information I have been able to learn about it has been, more or less, personal anecdotes and hypotheses based on them. I'm not sure how beneficial the change was because I don't have the "old" Lectionary to compare it with: in most cases, I suspect the change was neutral in its effect, but in at least one place it is definitely an impoverishment (but this has to do with a Gospel reading, and not with the letters we are discussing).
At any rate, whether or not the disputed catholic epistles are in the Peshitto, the Syriac Bible endorsed by the Patriarchate contains them and they appear in the canonically accepted order. This edition does not, however, contain some of the books which Mor Dionysius Vattaseril listed as part of the NT canon of the Syriac Church (those books are also not read from in any liturgy). This Bible also apparently rejects the Pauline authorship of Hebrews, contrary to the tradition of the Syriac Church. Furthermore, in at least one place (7 Sept), this calendar
lists a liturgical reading from II Peter, so even the Syriac Church seems to have adapted its practice. All in all, an interesting subject, but very difficult to generalise about.