The noun series is in order from Euclyca, Exiori and Elruna. Euclyca is technically Solenars Edge III, since it contains stuff and characters after it, but also contains characters from my other games. Although playing the other games in order does help, you don't need to play them to enjoy Euclyca, Exiori or Elruna, but it certainty enhances it.
Team Syukino Main series connection order: Solenars Edge: Last Song, (Included for free inside of Solenars Edge II: Aurora of The Seventh Dawn). Solenars Edge: Balthus Requiem, (Included for free inside of Solenars Edge: Rebirth). Luvocious, Solenars Edge: Rebirth, Restoration, Falnarion Tactics, Falnarion Tactics II, Solenars Edge: Afterstory (DLC), Solenars Edge II: Aurora of The Seventh Dawn, Restoration: X, Aeloren Tactics, Euclyca, Exiori, Elruna, (included for free in Exiori). The last in the series is Falnarion Tactics III. Each game can be played on it's own without having to play the others and some direct sequels should only be played after you played the prequel of it. However, playing all of these games, does enhance the overall plot and experience.
All the TS games share the same universe and there are some characters within some games who can travel between worlds. On another note here are some games that are non-cannon to the over all main universe series, even if they contain characters from other games, their story doesn't connect with the rest. Sometimes they might have some small details that do. Like the name of a character's parent from another game, etc like an Easter egg or cameo.
Non-Cannon List: Solenars Edge Heroes, Fesnia, Restoration Extra (DLC), Estellium Legends, Tales of Beasteria, Deatherem, Hentai Girl Slide Puzzle, Anetona, Solenars Edge II: Champions, Falnarion Tactics: Oathbreaker, Pixel Boy: The Legend of Tain, Four Hopes, Soneraka Online, Warfield, Fighting Spirit, The Judge, Estellium Legends II.
I hope this helps and answers your question.