Many industrial applications with real-time demands are composed of mixed sets of tasks with a variety of requirements. These can be in the form of standard timing constraints, such as period and deadline, or complex, e.g., to express application specific or non temporal constraints, reliability, performance, etc. Arrival patterns determine whether tasks will be treated as periodic, sporadic, or aperiodic. As many algorithms focus on specific sets of task types and constraints only, system design has to focus on those supported by a particular algorithm, at the expense of the rest. In this paper, we present a method to deal with a combination of mixed sets of tasks and constraints: periodic tasks with complex and simple constraints, soft and firm aperiodic, and in particular sporadic tasks. We propose the use of an offline scheduler to manage complex timing and resource constraints of periodic tasks and transform these into a simple EDF model with start-times and deadlines. On top of the offline schedule, sporadic tasks are guaranteed based on their worst-case activation frequencies. Then at run-time, an extension to EDF ensures feasible execution of tasks with complex constraints in the presence of additional tasks or overloads. It allows changes in the offline generated schedule to insert soft and firm aperiodic tasks by shifting the execution of offline scheduled tasks within their feasibility windows. Furthermore, the online algorithm uses the exact knowledge about sporadic arrivals to reduce the pessimism introduced by worst-case assumption, i.e., the resources unused by sporadic tasks are reclaimed to improve response times and acceptance of firm aperiodic tasks. A simulation study underlines the effectiveness of the proposed approach.