Since I need to use many different input methods at the same time so I wonder if there is a way to switch input method faster than pulling down the notification bar and clicking select input method?
If you are running on version 4.x you can change it from the notification bar or if your running on 2.x you can hold down where you are inputting the text and change it from there.
Select Input Method apparently lets you open the IME dialog via a single long press on the Search button. You can use the SIM Test to try this out before paying for the app. However, since most modern phones don't have a Search button, this app has limited usefulness.
Comments suggest that Pie Control can provide a soft Search key which can then be used to activate Select Input Method. However, I found that I was unable to map Search to a "slice of Pie" on my 4.1.2 Galaxy S3 (despite being able to map other controls like Home).
On Android 6 and later you can configure a keyboard change button to appear in the control strip alongside the soft Home and Back buttons whenever input mode is active. But if you have physical Home/Back buttons this probably won't work.
If you are rooted then you can flash a custom ROM such as SlimRom (https://slimroms.org) where you can assign the keyboard change action to long/double tap on Home or on the Back button.