With　the　rapid　development　of　5G　technology　in　recent　years,　multimedia　communication　services,　such　as　live　online　and　short　video,　have　received　wide　attention　and　become　the　important　means　of　people＇s　daily　social　intercourse.　However,　the　rapid　growth　of　multimedia　communication　demands　pose　greater　challenges　to　both　the　wireless　network　communication　capacity　and　the　network　processing　capacity.　Mobile　Edge　Computing　(MEC)　is　widely　regarded　as　a　promising　technology　to　cope　with　the　above　challenges.　To　satisfy　the　growing　demands　and　improve　the　quality　of　experience　for　users,　it　is　in　urge　need　to　seek　the　effective　and　efficient　task　assignment　and　computing　offloading　strategy　for　MEC　networks.　In　this　paper,　we　focused　on　the　multimedia　services　which　need　to　be　processed,　uploaded　and　shared　in　the　network　and　research　the　long-term　task　assignment　and　resource　coordination　problem.　We　formulate　the　optimization　problem　as　a　stochastic　optimization　problem　with　the　aim　of　the　minimizing　the　time-average　energy　consumption　of　the　system.　By　using　the　Lyapunov　optimization　technique,　we　decompose　the　original　problem　into　several　subproblems　which　can　be　solved　with　current　system　information　and　low　computational　complexities.　On　this　basis,　we　propose　an　online　energy-efficient　task　assignment　and　computing　offloading　strategy　to　adaptively　decide　the　task　assignment,　coordinate　and　optimize　the　wireless　and　computation　resource　allocation　by　taking　the　dynamic　wireless　condition　and　service　delay　constraints　into　consideration.　Extensive　simulation　results　show　that　our　proposed　algorithm　can　achieve　considerate　energy　consumption　and　delay　performances　under　different　conditions.