Mobile　Edge　Computing　(MEC)　provides　a　new　opportunity　to　reduce　the　latency　of　IoT　applications　significantly.　It　does　so　by　offloading　computation-intensive　tasks　in　applications　from　IoT　devices　to　mobile　edges,　which　are　located　N-close　proximity　to　the　IoT　devices.　However,　the　prior　researches　focus　on　supporting　computation　offloading　for　a　specific　type　of　applications.　Meanwhile,　making　multi-task　and　multi-server　offloading　decisions　in　highly　complex　and　dynamic　MEC　environments　remains　intractable.　To　address　this　problem,　this　paper　proposes　a　novel　approach　called　MultiOff.　First,　we　propose　a　generic　program　structure　that　supports　on-demand　computation　offloading.　Applications　conforming　to　this　structure　can　extract　the　flowcharts　of　program　fragments　via　code　analysis.　Second,　a　novel　cost-efficient　offloading　strategy　based　on　a　Multi-task　Particle　Swarm　Optimization　algorithm　using　the　Genetic　Algorithm　operators　(MPSO-GA)　is　proposed.　MPSO-GA　makes　offloading　decisions　by　analyzing　program　fragment　flowcharts　and　context.　Finally,　each　application　can　be　offloaded　at　the　granularity　of　services　with　the　offloading　scheme,　minimizing　the　system　cost　while　satisfying　the　deadline　constraint　for　each　application.　We　evaluate　MultiOff　on　several　real-world　applications　and　the　experimental　results　show　that　MultiOff　can　support　computation　offloading　for　different　types　of　applications　at　the　fine-grained　granularity　of　services.　Moreover,　MPSO-GA　can　save　about　2.11-17.51%　system　cost　compared　with　other　classical　methods　while　meeting　time　constraints.