I don't think the order matters, just that you get all CGs.
I noticed, that sometimes, depending on whether you favor Natsuki or Yuri more, by the 3rd poem, the other may completely ignore you based on poem order. I've had this happen once for both girls.
On my first play through, I focused on Yuri, I would show her my poems first and then the other girls. By the 3rd poem exchange, Natsuki was so pissed off with [me/my character] that she refused to even talk to me. This also happened on my last play through when I focused more on Natsuki and had Yuri very upset with the character as well.
With the other play throughs, if I saved the poem for the girl I was focused on last, then I wouldn't see any problems during exchanges. Just a pretty interesting if/else code segment setup in the design (I found it fascinating as I'm a programmer myself).
Yes, depending on how you score, you might get either a 'meh' or a negative reaction. It doesn't affect the game much though. You still need to go through all 3 routes to get all the CGs... I think.
I mean... The Sayori hug CG you get whatever you do. (Well, not really, but you can get it any route). And you need to play twice to get the CG from your place... But the other 2 per character need to be done by writing poems for the respective girls... so yeah, still need to do the poems 3 times.
EDIT: I think it's possible to flavor one girl without making the others pissed at you. Just pick 2-3 words for the girls you don't chose and the rest for the one you do... should work.
After realizing this was an ARG, I started looking around in the files that were easily accessed. One such file "game\scripts.rpa", when opened has an opening poem "There's a little devil inside all of us." When you scroll down, there is a bunch of RENPY [garbage] for whatever reason. If you scroll even further down to line 4149, you'll get access to winning words for each of the three girls.
The interesting part is that it appears each word bears more weight depending on the act. Where Sayori seems to get the most impact in act 1, Natsuki in act 2, and Yuri in act 3. Oddly enough, Yuri has a lot of words that are 1,1,3 when chosen. So it seems especially difficult to draw her attention in act poems 1 and 2 if you accidently pick Sayori/Natsuki words. That being if each word, the number indicates a value and is totaled at the end of the poem creation.
Now that I'm reviewing the file again. At the bottom, there is huge section of characters. I just took it to a Base64 converter and found out that it's the small wooden box story. Heh, go figure.
Yeah, I meant to say the poem portions of the 1st, 2nd and 3rd poems you're to create in Act 1. I wrote too fast and didn't go over what I had written. For example
Candy1,3,2
I'm guessing this means that for Natsuki, Candy would only add +1, +3, or +2 points to the total poem score depending on which poem this was being written for in the 1st act.