“I went straight home after work.”

You usually stop by the supermarket or the gym after work before coming home. But yesterday you wanted to get home earlier because you are hooked on a TV show that you've been watching on DVD. You tell your friend

I went straight home after work to watch it.

go straight (to somewhere)

To "go straight to" somewhere means going there directly, without going anywere else on the way. Notice that you use "to" with most destinations:

went straight to work

go straight to the police station

go straight to my house

However, "home" has its own special rules. You shouldn't use "to" with "home":

go straight home

after work

When talking about your job as an activity during your day, you should use the term "work" - not "my job", "my work" or any other variation.

I had an interesting coversation at work today.

She goes running in the morning before work every day.