They have meanings that partially overlap. That means that in some contexts they are interchangeable but in some they aren't. For example, I might suggest or recommend a good restaurant; I'd advise you against eating at a bad one. In this context, suggest and recommend have similar meanings (though 'recommend' suggests I've been there before). "Advise" is stronger. If there are two restaurants, one good and one bad, I'd advise you to go to the good one. I would think it a mistake if you didn't take my advice.
But in other contexts the overlaps would be different. Use a monolingual dictionary (and read as much as you can) to get an idea of the differences.