The key conceit of Iljena is that all words encode both a nominal root and a verbal root--and based on both the grammar notes and the dictionary, there are no other parts of speech. All verbs are monovalent, and you construct large propositions by chaining together noun-verbs that describe what each participant is doing. It's sort of like the disambiguation strategy sometimes employed in natlangs where a transitive clause that lacks distinctive subject and object marking (like two neuter nouns in a positive-polarity Russian sentence, or nouns with equal animacy in a direct-inverse language) can be split in two with an antipassive clause and a passive clause--i.e., instead of "Bob saw Bill", "Bob saw, Bill was seen". Except that Iljena doesn't have a passive construction, it just has enough different verb roots to cover all the necessary meanings, whether one is an agent or patient or instrument or whatever in any particular scene.
With the lack of any other parts of speech, however, it is unclear how boundaries between clausal constituents are determined, how attachment ambiguities might be resolved, or how references to events-as-things are made, and the only ordering constraint is that
Word order is used to convey the flow of the action between the participants, and to bring together closely related participants.
However, David Gil has shown us that you don't really need to formalize all that grammatical machinery all of the time, and the corpus of Conlang Relay texts in Iljena, which have been translated reasonably faithfully by following relay participants, demonstrates that it does work well enough. Pete's own documentation notes that Iljena could be considered a "verbless" language, based on the idea that verb roots could instead be interpreted as noun cases (which is one of the possible solutions to verblessness I discussed in my own article How To Not Verb), but he (and the fictional Leyen people who speak Iljena) prefer to think of the relevant open lexical class as verb roots, rather than case morphology--and I tend to agree. The complete lack of function words makes Iljena a decidedly non-human language, but that's fine--it's not supposed to be!
As noted, Iljena does seem to work just fine as it is, so I won't presume to suggest improvements--but I think it would be neat to see a language that takes the one verb--one noun approach and embeds it in a larger system of grammatical function words for eliminating structural ambiguities. And it would also be neat to see some more detailed analyses of the existing corpus texts, beyond simple interlinear glosses, that might be able to extract more empirical rules about Iljena grammatical structure.
