中文問題....

遊的詞義:
1.to tour; to travel; to go to a distance(＊）
2.to roam; to saunter
3.to associate with people; to befriend; to make friends
4.to have fun（＊）

悠的詞義:
1.long-drawn-out; remote in time or space
2.leisurely（＊）
3.[Informal] to swing
4.sad; pensive; meditative

由的詞義:
1.cause
2.because
3.by or through
4.to follow the wishes of（＊）
5.to allow or entrust someone to do
6.from

所以,
自遊行:自行旅遊(一般情況都應該是這個用法)
自由行:自由地行走
自悠行:自在從容的到處遊覽

我諗無對或錯之分, 只是你想表達什麼意思. 三個同樣可用.