Is it possible to auto-generate Javadoc comments for each method in one class in IntelliJ IDEA?
Yes.
Under Tools you have Generate JavaDoc. Read about it in the official site.
In addition you may (Intellij 15):
Position caret above a method name, type /** and press Enter to let IntelliJ IDEA automatically generate JavaDoc stubs for this method
Edit: You can use the action Fix doc comment. It doesn't have a default shortcut, but you can assign the Alt+Shift+J shortcut to it in the Keymap, because this shortcut isn't used for anything else.
A QuickShortCut is
CTRL+SHIFT+A 
 From the dropdown List "Fix doc comment"
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