I have massive amounts of organic traffic, but I am struggling to monetize my app and website.
Not knowing what type or vertical you are in, it is difficult to say how.
100,000 visitors a month is a decent size. Most people opt for placement of banner ads and affiliate links and it works for them. However, you might also look at other avenues of monetizing.
One of the most important aspect is to understand "why" they are visiting? What is their bounce rate? Are they looking for information? Are they downloading something? Building a better profile of your audience will pay you back ten folds over. Understand your audience and then cater to their needs. You surely have managed to get their attention, now get them to engage with you more. Proper placement of CTA (Call To Action) buttons could build your mailing list or have them fill out a form or even allow you to do A/B testing by asking people to give you a survey answer, right there on the website itself.
Data drives decisions!
The more data you have the more options you have as how to work with it.
Again, not knowing what your 20,000 App downloads is all about, it is very difficult to say how to monetize without the needed a prior information.
Pay attention to your visitors, build their profile as accurately as possible and use services like SomoMe to generate heat-maps of what they are doing, where they are clicking most, etc.
The more you know about their behavior, the more you can strategize towards monetization.