How do I remove multiple layers of paint from wooden entrance ledge?
One of the best tools to begin the process of removing old, thick paint is a simple hand scraper



I would remove the metal strip, if possible, and use the scraper to remove most of the finish. The edges on the scraper can be rotated as they get dull.

Then you can follow up with either stripper (there are new citrus based that are pretty effective if you let them sit), or an orbital sander.

If it is very resistant, you could use a multitool with a scraper blade or even the grinding plate if it is very hard. This is an example, but there are many simpler and cheaper versions. 



Caution with the multitool because once you cut through the paint, the wood may gouge or tear.