Unfortunately, the Syndrome games have never been re-released or translated. A fan-made patch to translate these games is also yet to surface at the time of this writing. However, there exist translated playthroughs on Youtube.
Youtuber aRdW has translated both Tansaku-hen and Kyuumei-hen.
I have archived both playthroughs so I can re-upload them in case they are taken down for any reason.
When it comes to Moonlight Syndrome, Izzeybee has translated the first half of the game on her blog. She allowed me to use her translations to produce a subtitled playthrough, which you can find in the following playlist. The second half of the translation is being handled by Jolovey. At the time of this writing, this is still a work in progress.
While I am not interested in covering the later Syndrome games, as Suda Goichi or Grasshopper Manufacture were not involved in their production, aRdW did produce a subtitled playthrough for the Spike-Chunsoft reboot, Saikai.
The final game in the series, Twilight Syndrome: Kinjirareta Toshi Densetsu for the Nintendo DS, remains untranslated.