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.
Re-visit your marketing strategy. Which is to say - re-visit your business model (which should very directly point you in the direction of your highest probability marketing strategy).
And (get ready to not like me for saying this...) stop focusing on those numbers. The number of visitors per month and the number of downloads are only relevant as they directly relate to conversions and sales.
And those things are only relevant as they directly relate to bottom line revenue and margins.
It's easy to get caught up in "vanity numbers"... those numbers that "feel good" and provide you with a sense of validation. But until and unless they translate into bottom line income for the business they are just numbers that make you feel good (versus wisely chosen key metrics that indicate the health and viability of your business).
If this was helpful to you please let me know how else I can be of assistance.
You need to create a marketing funnel that gives you several levels of conversions. I tend to name these Lead -> Prospect -> Activated Customer -> Repeat Customer. Organic traffic is all well and good, but is it targeted and segmented? You could have an information products business or an affiliate marketing business or one of several other business models. It all comes down to evaluating your site and seeing where the value is for some segment or segments of your audience in order to engage them in a buying relationship. Customer activation is without question the most important piece of a business like this. Happy to discuss with you if you'd like.