First off, the meaning of jutsu 術, because, after all, if there is one thing ninjutsu, taijutsu and genjutsu have in common that would be precisely the jutsu.
A jutsu 術, also spelled jitsu in English, is an "art" or "technique" which can be applied to do stuff and things. Unlike waza 技, which would be a specific "technique," the word jutsu is used as a way to categorize or generalize things.
Alone, jutsu can mean a random "trick" or "magic" of sorts, but when used as a suffix, it says something like "a discipline which you train real hard to learn so that can do this sort of thing." See:
- shujutsu 手術
Surgery. Surgical operation.
- juutsu 柔術
Jiu Jitsu. Japanese martial art.
- geijutsu 芸術
- gijutsu 技術
- senjutsu 戦術
Tactics. Battle arts.
- majutsu 魔術
Black magic. Magical arts.
All of those things above are things you have to learn so you can perform things. They are, each of them, an art and/or a science.
The word ninjutsu 忍術 means pretty much "the art of the ninja." I mean, literally, "ninja" in Japanese is just ninja 忍者, and the ninjutsu would be the art that made a ninja a ninja, an art exclusive to ninjas.
In anime such as katanagatari 刀語 ninja techniques are often referred to as ninpou 忍法 instead of ninjutsu.
In the anime naruto ナルト, the ninjutsu were probably the techniques which were most ninja-like. I mean, the taijutsu and genjutsu had nothing to do with ninjas, after all.
The word taijutsu 体術 would be the art of the body, since the first part, tai 体, has the same kanji of the word for "body," karada 体. By the way, jintai 人体 is an "human body," and taijuu 体重 means "body weight" in Japanese.
In naruto ナルト the taijutsu 体術 were all about martial arts and punching and kicking stuff. As far as the show was concerned, as long as you used your body to assassinate people and not some funky chakra shenanigans it'd be considered taijutsu.
(see also: names of body parts in Japanese)
The word genjutsu 幻術 would usually mean "witchcraft." Following the meaning of the suffix jutsu, and considering that genkaku 幻覚 means the sensation of "hallucination" and gensou 幻想 means "illusions," genjutsu can only be something which you train for to make these illusions. And if it isn't "hypnotism," saiminjutsu 催眠術, then it ought to be "witchcraft!"
Ironically, in naruto ナルト the genjutsu were actually like hypnotism. By using their magical ninja powers, ninjas would spawn illusions out of thin air to confuse their foes, which matches the literal meaning of the word.