Omega makes a decision to put the money in the box, or not. In my model of (MWI) reality, that results in a branching - there are now 2 worlds (one with money, one without). The only problem is, I don't know which world I am in. Next, I decide whether to one-box or to two-box. In my model, that results in 4 possible worlds now. Or more precisely, someone who knows neither my decision nor Omega's would count 4 worlds.

Incorrect. Omega's decision is no more indeterministic than the output of a calculation. Asking (say) me "Does two plus two equal three?" does not create two worlds, one in which I say "yes" and one in which I say "no" - overwhelmingly I will tell you "no".

Your model ought to be branching at every subatomic event, not at every conscious intelligent choice.

This makes reality (even humans) predictable.

As others have said. Omega-talk is possible in a purely classical world, and is clearer in a classical world. Omega simply scans my brain and deterministically decides whether to put the money in or not. Then I decide whether I take one or two of the boxes. To say my choice should not have any causal influence on his choice is misleading at least. It may be true (depending on how exactly one defines causality), however it doesn't exclude correlations between the two choices simply because they are both consequences of a common cause (state of my brain and the relevant portion of the world immediately before the scenario begun).

There is no need to include quantumness or even MWI into this scenario, and no certain reason why quantum effects would prevent it from happening. That said, I don't say that something similar is probably going to happen soon.

That's the case if you somehow manage to use a quantum coin in your decision. Your decision could be close enough to deterministic that the measure of the words where you decide differently is billions of times or more smaller and can safely be neglected.