Don't say 别人之委托, which sounds a bit awkward. Instead, say either "别人之托" or "别人的委托". The reason for that is simple. 之 was originally from Classical Chinese. So was 托, like many other ONE-character words. However, 的(used to mean "of") and 委托 were minted in the 20th century. Therefore, it's not suitable to mix a Classical Chinese word with a modern Chinese one, which Chinese people criticize as "文不文,白不白". Your 2nd and 3rd sentences are both correct, but I'd suggest removing "到" from "受到".

2种说法其实是一个意思. They're all right. ‘委托'是相对正式（formal）的说法. 单独使用 ’托' 则比较口语话，这里的‘托’ 正是 ’委托‘ 的意思，因此理解成缩写也可以。

There are not significant difference between two sentences. Don't let it confuse you. Usually, "之" is widely used in ancient written Chinese and it is also used nowadays. You are confused because someone told you that you cann't say ... Maybe the only rule for this is : when you use two characters, choose 的， when you meet one character, use 之, but in most case, you can also use 的, not the reverse。 for example, 受朋友之“恩”=受朋友的“恩惠”。 受人之托 is more like an idiom. we rarely use such structure in other cases. so just remember this.