The key here is that you are looking at a project. If you are looking at projects, the sorting controls sort projects, not actions. The context view sorts actions.
Do you want to permanently change the order of the actions in the project? You can select the actions you want to re-order, then choose Edit->Sort->(what you want to sort by) and OmniFocus will re-order them. This is different than using the View Bar controls, which only change the view; Edit->Sort is like dragging the actions into the specified order.
So, if you want to look at all of your actions, and see which ones start first, go to Context mode, and sort or group by start date. That will combine all the actions from your various projects, sort them by start date, and show you the list. If you have a project where the sequencing is not important, and you want to re-order the actions so the ones with the earliest start dates are at the top, go to Project mode, select those actions, and do Edit->Sort->Start Date.