“Walk” is by far the most common and most general of these words. Examples: “I walked five miles today.” “After the car crash, he no longer is able to walk.” “My car broke down so I had to walk home.” “Stroll” is used specifically to refer to slow, leisurely walking. You would not use “stroll” in any of the examples above. But, you might say: “My wife and I took a stroll along the beach today. The weather was beautiful.” It is a common word, but much less general and less frequently used than “walk”. “Promenade” is almost never used as a verb, at least in the US. Sometimes you hear it as a noun — with the last syllable rhyming with “rod” to make it sound French — to refer in a fancy way to a place to go walking. Example: “Our hotel has a beautiful tree-lined promenade from which guests can see the ocean and beautiful sunsets.”

As a native English speaker, it is uncommon to use the word 'promenade' to describe a leisurely walk. I have heard 'promenade' used to describe an outdoor mall or walkway. 'Walk' and 'stroll' are more commonly used. Some examples are: 1. Would you like to take a walk in the park with me? 2. I went for a nice stroll this evening. I hope this answer is useful to you. Let me know if you have further questions!