Population will never step growing. We will likely (try to) expand into space, onto the oceans, or below them. Invincibility and no need for food would make it a lot easier than now, and there will be more pressure due to growing population.
Reproduction is an instinct, both sexual and social (need to care for somebody, need to make "copies" of oneself). There is nothing in your setup that limits this instinct.
Normal limitations for unlimited population is lack of food, disease and war. You have ruled them out.
Earth will get more and more crowded, but that will not stop the reproduction instinct. We see people continue reproducing even when they have low income, live in a war zone, etc.
High-income people usually have fewer children (no good explanation, maybe they are too busy making money, maybe they prefer to invest more into each child). But perfect health and infinite lifespan will make them continue reproducing as well.
Edits, or rather additions:
The premise of "indestructible" and "no sustenance" violates basic physical laws (conservation of energy). I am glad you realize it takes divine intervention to make it happen. After that, both your readers and the people in the story will expect further miracles to aid in their struggles.
Here is a better way to introduce such plot devices.
Unlimited population growth will lead to resource shortages. Humans will still need houses, cars, clothes, entertainment. And they will still want to have a better life than their neighbors.
There will be an immediate economic crisis worse than the Great Depression of 1930's. Back then, engines and tractors eliminated some of farming jobs. Now, you eliminated all the jobs in farming, food processing, food retail and restaurants. Huge unemployment among low-skilled people, who have very little chance of re-training (unlike the doctors). To avoid revolution, we will need huge welfare programs, or massive public works (maybe US will fix its potholed roads).
Developed world might eventually find a way to keep population growth limited, so technological innovation can keep up. E.g. have a limited number of reproduction licenses available either through free lottery or large fee. Violators will be force to pay the fee, kicked out of the country, or sterilized. This will work best in small, isolated and mono-cultural countries with tradition of law and order, e.g. Scandinavia or developed nations East Asia.
Third world countries will descend into wars over limited resources (using excuses of religion or ethnicity). You cannot kill people, but you can bury them alive or throw them into the ocean (in shipping containers, with a few bricks for ballast).
If people know that it was Christian God who did it, there will be a lot of mixed feelings, including anger over the side effects. Also note that Jews and Muslims are technically worshipping the same god; they just disagree on who's the true prophet.
Final edit. I decided to lighten up, and come up with a viable solution to some of the problems I found. All the healthcare spending of the developed world is re-routed to returning farmland back to natural state, planting trees, breeding wild animals, etc. This keeps former farm workers employed, at least long enough for society to create new jobs for them, e.g. in eco-tourism. As for population control, make welfare and public-works jobs require a birth-control implant.