Refers to a way of doing something, often implying a skill or know-how. Commonly used in expressions like ～すべがない (there is no way to ...).
There is no way to contact him.
Acquire the means to live.
There was no way to check on the safety of my faraway friend.
He didn't know any way to fix that machine.
手段 refers to a concrete measure or tool used to reach a goal, whereas 術 (すべ) is more abstract, often describing a last resort or ability to cope.
手立て is a practical measure or resource one can use, while 術 (すべ) leans toward the idea of any conceivable way, frequently in phrases like なすすべもない.
Written with the same kanji, 術 read じゅつ means a skill, art, or technique (e.g. 忍術), while 術 read すべ means a way or means, almost always in negative expressions like すべがない.
Usually written in kana; the kanji form 術 is also used but less common.
Kanji spelling; can also be read じゅつ in other contexts.
The origin is uncertain, but it is a native Japanese word. The kanji 術 is an assignment based on meaning, not etymology.