Les Heures Grégoriennes = a Latin/French antiphonary for the Liturgy of the Hours, Latin is on one page, French on the facing page. It was produced by the Communauté St-Martin in France for their own use (they train priests), but it is licit and fulfills the obligation for others who are obligated to the LOTH. It only contains the day hours (Lauds, Terce, Sext, None, Vespers and Compline), not the Office of Readings.
An antiphonary is the Liturgy of the Hours, or the old Breviary, set to music, in the above case, Gregorian chant. Les Heures is for the current (post-Vatican II) Liturgy of the Hours.
Antiphonale Romanum I and II are the first two official volumes of the Latin antiphonary for the Liturgy of the Hours. They are Latin only. There will be other volumes to follow, God only knows when.
Recto-tono is chanting in a monotone. It is the simplest form of plainchant and can be done if you don’t have an antiphonary, or are not skilled in more complex chant,
The Nocturnale Romanum (if one is ever completed, mine is home-made) is not for Compline, it is an antiphonary for the Office of Readings which replaces the old night office of Vigils (or Matins), and which still contains its “nocturnal character” (General Instruction for the LOTH).
Ordo Cantus Officii is the official list and source of Gregorian chants for the Liturgy of the Hours, It cannot be used to pray the Office, it is a reference for those creating their own LOTH chant books (many religious communities have their own house books). The first edition was, I believe 1983. The second is 2015. It specifies which hymns, antiphons and responsories to use, Antiphonale Romanum I and II follow the schema laid out by the Ordo, and Les Heures Grégoriennes does as well with some simplifications (repetitions).
Hope that helps!