hide parameters passing to controller in address bar (URL rewrite or something else)

You could use POST instead of GET. So you could replace the link with a form containing hidden fields for the parameters that you don't want to appear in the query string:

@using (Html.BeginForm("EventOverview", "BaseEvent", new { id = eventInfo.Key.OID, type = eventInfo.Key.XPObjectType.TypeName.GetShortTypeName() }, FormMethod.Post, null))
{
    @Html.Hidden("activeTab", "#scheduleLink")
    @Html.Hidden("session", eventInfo.Key.EventSchedules[0].SessionId)
    @Html.Hidden("hall", eventInfo.Key.EventSchedules[0].HallId)
    @Html.Hidden("client", eventInfo.Key.EventSchedules[0].BasePlace.PremieraClientId)
    <button type="submit">Make</button>
}