上司から多くの仕事を頼まれたって英語でなんて言うの？

The first example here is probably the most correct and informative, the second and third examples are more commonly used to avoid committing to further tasks. The last suggests a beast of burden and has a slight connotation of complaint.

*My boss has given me a lot of work to do.- This is a simple way of expressing yourself. *My boss has loaded me with a lot of work. - In this case loaded means to be given a lot of work. It can also be used to refer informally to have a lot of money. For example "He is loaded."

It depends whether you feel aggrieved or unhappy with your work load. The first sentence is quite objective, however the second sentence is critical.

An idiom...or two..can come in handy to express clearly what we mean:-D In this case..."A ton of work" is used in a figurative sense, as is the phrase " gone overboard" We can depict our situation more dramtically with these kindd of phrases;-) "My boss has really gone overboard on me, giving me a ton of work to do!"

By using the term 'My boss' it explains who gave you the work. So you could say 'My boss gave me a lot of work to do' or 'my boss asked me to do a lot of work' both meaning the same thing you have been asked by 'your boss' to do more work

If you want to explain that your boss gave you a large amount of work to do you can say, "My boss has me doing so much work."

The two sentences you see provided above are great ways to express to your listener that your boss gave you a lot of work to do. In the first sentence you will notice the verb overload. This means to give more than what one can handle. In the second sentence you will notice the word ton. We use this word in a figurative way to describe a large amount of something. So if your professor gave you a lot of homework you can say you have a ton of homework.