The federation between cloud and edge has been proposed to exploit the advantages of both technologies. However, the existing studies have only considered cloud-edge computing systems which merely support vertical offloading from edges to clouds in one direction. However, there are certain cases, where the offloading needs to be done from clouds to edges and between edges. Such a cloud to edge offloading is called reverse offloading. To this end, this paper proposes a generic Omni-directional architecture of cloud-edge computing systems intending to provide vertical and horizontal offloading. To investigate the effectiveness of the proposed architecture in different operational scenarios, we formulate the dual cost optimization problem with different latency (loose, low, ultra-low) constraints. We develop an offloading algorithm using simulated annealing (SA). The experimental results show by our proposed OMNI architecture we can reduce the total cost by 15-25% and 10-20% in non-uniform and uniform inputs, respectively, compared to other existing architectures. The average latency in OMNI architecture is relatively very less compared to other architectures. It also increases utilization in the edge nodes by 5-30% in comparison to other existing architectures.