最简单的记忆是：
fall down 倒下, 跪拜
fall over 落在...之上, 脸朝下跌倒,向前摔倒
fall off 下降, 跌落, 减少, 衰退, 离开
细致分析：
fall down,fall off和fall over都表示“摔倒、跌倒”的意思,但它们各自的含义不同.
1.fall over强调的是“向前摔倒、跌倒”.
She fell over and broke her leg.
她跌倒并把腿摔断了.
There is too much snow on the ground. If you ride much too fast,you will fall over.
地上的雪太多,如果你骑得太快的话,你会摔跤的.
2.fall down强调的是“滑倒、倒下”,后接宾语时应加上介词 FROM.
The boy hit the tree to hard that he fell down.
男孩重重地撞在树上,结果自己倒下了.
If people run across the road,they may fall down.
如果人们跑过马路的话,他们可能会摔倒.
3.fall off强调的是“跌落、从……掉下来”,后直接接宾语.
The girl is falling off the bike. （= The girl is falling down from the bike.）
女孩正从自行车上摔下来.
They spread a big net in case Tom should fall off the tree and get hurt.
他们张开一张大网以防汤姆从树上掉下来受伤.