I do not think it is entirely a case of religion having an evolutionary strategy, (though it does), so much as evolution not having a strategy for religion. Evolution only works retrospectively, if you survive the challenge of a change in your environment at all, then you get better at meeting the challenge over time, but natural selection can not foresee the challenges beforehand. And no animal ever met quite such a big change in their environment quite so quickly as humans did when they invented, first language and then culture. We have therefore no evolved tools from nature to deal with these things, and are thus ready made victims for anyone, (religious, political or commercial) who can manipulate language and culture.

Cohesive tribal groups are more likely to survive and, therefore, breed. That which aids cohesion thrives.

Evolution has no agenda or goal and evolution is not necessarily progress. Natural selection and survival of the fittest also does not necessarily mean survival of who is "right". For example, The Catholic Church terrorized and coerced people into having more children than they can afford. This still goes on today. On day, evolution may select out those who have certain religious beliefs. Those religions who refuse medical care are good candidates.

Eventually I think all religions will fall to the realms of myth, which they all are. Unfortunately evolution is painfully slow in getting there.

Evolutionary strategy for religion? I doubt there is one. However, Most religions have several goals in common. They are: to survive, continue to grow, help people, save souls, and become more influential. But, I am not sure if this is what you mean by evolutionary strategy. Is it?
You say no society without religion has survived. I question that. China and Japan are, for the most part, atheistic/agnostic when it comes to believing in a supernatural deity. This is also becoming true for Europe and North America according to the poles.
My personal theory is that as societies become more reliant upon and trusting of science, they tend to be less religious. Evangelical religions are currently fighting for influence and survival. Many believe our President is their hope for making America a Christian nation.

The missions statement for most of them?

1. Breed more followers and don't ask too many questions.
2. Get them to breed more followers and not ask too many questions.
3. Get them to breed more followers and not ask too many questions.
4. I think you get where this is going.

Religion doesn't really have a plan beyond that. Just keep pairing 2 people together, hope that they produce more than 2 offspring, raised to stick their fingers in their ears and shout 'la-la-la' very loud at the suggestion that the whole thing might be nonsense, and to also breed more than two offspring. The congregation increases exponentially with each generation (especially if you encourage large families.) Happy days.

I think religion is just an outgrowth of our intelligence. We have active minds, they can't always fully engaged in the literal world so they start making up stories and sometimes take them a little too seriously.