For a while now, newer versions of Visual Studio have been able to display in-line information for methods, fields etc relating to how many times they may have been referenced or changed and who changed the code last. This feature is known as CodeLens.
Is there any plugin or feature in IntelliJ IDEA similar to this that would be able to display information on an individual class/field/method basis?
There is no such plugin (yet).
You can of course right click the left gutter (gray editor to the left of the editor) and select "Annotate". That gives you at least the last edit per line.
More similar to your desired feature (but unfortunately not inline): Select some text (e.g. a method), then right-click Git -> Show History for Selection.