If someone has an average of 1 litre of Coke or Pepsi a day, would this form too much benzene oxide in the person's body or stomach and eventually effect part of their genetics?
Benzene oxide isn't present in Coke or Pepsi. Some drinks contain sodium benzoate though. If that is what you're concerned about, there's not really any cause. Sodium benzoate is not remotely harmful in the concentrations that humans ingest. Here is the FDA's statement on benzoates and benzoic acid.
There were claims that a mixture of ascorbic acid and benzoates would react to form benzene. That has been shown to not be an issue. There were ~100 drinks containing benzoates tested by the FDA, and only 5 showed benzene levels higher than allowed in drinking water. These were reformulated and now show less than 5ppb benzene. I would suspect that their benzene came from another source rather than this unlikely reaction, but I don't have any evidence for that.
Finally, neither Coke nor Pepsi even contain benzoate, benzoic acid, or any other compound that is chemically close to benzene.