Integrated sensing and communication (ISAC) is a key technology for future 6G networks. Most existing studies focus on monostatic and/or bistatic setups with limited coverage and capabilities. Networked ISAC systems with distributed base stations (BSs) can overcome these limitations. Moreover, movable antenna (MA) architectures offer improved ISAC performance over fixed-position antennas (FPAs) by enabling adaptable antenna movement. In this paper, we utilize the MA to promote communication capability with guaranteed sensing performance via jointly designing beamforming, power allocation, receiving filters and position configuration of transmit/receive MA towards maximizing the sum rate for both downlink (DL) and uplink (UL) users. The optimization problem is highly difficult due to the unique channel model derived from the position coefficient of the MA. To resolve this challenge, via leveraging the cutting-the-edge majorization-minimization (MM) method, we develop an efficient solution that optimizes all variables via convex optimization techniques. Extensive simulation results verify the effectiveness of our proposed algorithms and demonstrate the substantial performance promotion by deploying the MA framework in the networked ISAC system.