How many of all possible English words are actually in use (have meaning)?

It depends on how you approach this. It would be relatively easy to generate English non-words using phonotactic rules and then calculate the proportion. As others have said, it is likely to be quite small even if we exclude arguments by recursion which generate unrealistic word forms no matter how supposedly well-formed.

However, something similar has been done in the Lexicon Projects for orthographic forms (for many languages these would be the same but for English they present completely different challenges). The American and British Lexicon projects. However, their aim was not to generate the largest possible number of non-words but rather the largest possible number of plausible forms that could be used in psycholinguistic testing requiring non-words.

You could possibly use their data to generate a more comprehensive list (e.g. by training a neural network on the patterns combined with some rules). However, I'm not sure if the pay off would be worth the effort - unless you can find some real application.

Also, the British Lexicon Project has done work on Dutch, German and French.