“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 this to your friend.
I went straight home after work.
To "go straight to" somewhere means going there directly, without going anywere else on the way:
I went straight to the hospital to see her as soon as I heard about the accident.
When talking about your job as an activity during your day, you should use the term "work" - not "my job", "my work", "my office", or any other variation.
I had an interesting coversation at work today.
You can use the phases "before work" and "after work" to talk about things that happen in the morning before someone goes to work or in the evening after they leave.
She goes running in the morning before work every day.
What are you doing after work?
The word "home" has its own special grammar rules. When you talk about going somewhere, you usually use "to":
Notice that you use "to" with most destinations:
I have to go to work.
We're going to New York at the end of this month.
But you shouldn't use "to" with "home":
I want to go home.
There are a few other words that behave the same way, like "here", "there", "somewhere", "anywhere", and "away":
Let's go there together.
Don't go anywhere.