Welcome.
Just a quick reply as I need to move. I've had a quick look on the web and all (there were lots of) the Drake (RF?) wattmeters I saw had traditional moving coil meters. Do not go anywhere near the meter with machine oil, you will ruin it!
Now please provide more detail - the model of the meter, a photo, more detail of exactly how the meter is behaving - is it in particular locations on the dial etc. You need to provide a decent level of information if you expect a reasonable level of help.
Edit: sorry, I missed the W4, but as I mentioned, the nature of the sticking, whether you've had it for years and it's slowly / suddenly come on. Whether you've just received it from ebay etc. are all relevant.