Hi ChangSeok, I would say 'I went straight home after work' (here 'work' is a noun, so you don't have to say 'after working'). You could also say 'I went straight home after getting off work'. 'After finishing work' is not something I often say, but it sounds perfectly natural. I would use 'directly' with 'go' when I'm describing a route from one place to another, or emphasising how I'm getting from one place to another. For example, if you want to go from Seoul to London, you can go via Moscow or you can go direct(ly). I hope that makes things a little clearer!