occupied/preoccupied

The president is much occupied with affairs of state.
总统总是忙于国事。

He occupied his whole afternoon reading documents.
他用了一下午的时间阅读文件。

overloaded

The bar waiter was already overloaded with orders.
这位酒吧侍者已经应付不过来客人的点单。

Faculty are in short supply and tend to be overloaded with work, limiting their capacity to undertake research.
教师供不应求，而且教学工作往往超负荷，制约了他们的研究能力。

tied up

He's tied up with his new book. He works hard till midnight every day.
他正忙他那本新书。他每天都工作到半夜。

My hands are tied. I must hand in my homework this afternoon.
我很忙，今天下午必须把家庭作业交上去。

I have EPA over both her financial affairs and her welfare, yet my hands are tied both her obduracy and that of the LA.
在她的金融事务和福利方面，我都有EPA。但LA政策和她的顽固让我无能为力。

in the middle of sth

What were you up to?
刚刚忙啥呢?
I was in the middle of serving a customer when you called me.
你给我打电话的时候，我正在忙着照顾一个顾客。

wrapped up in

He's too serious and dedicated, wrapped up in his career.
他太严肃、太专注，一心扑在事业上。

Nowadays, lots of Canadians and Americans are wrapped up in their small world and know little about China.

all wound up

You won't fall asleep if you're all wound up from answering email, or doing other work.
如果你在睡觉前还在忙着回复邮件或者做其它事情，那你肯定睡不着。