In the era of 5G, with the increasing demands on computation and massive data traffic of the Internet of Things (IoT), mobile edge computing (MEC) and ultradense network (UDN) are considered to be two enabling and promising technologies, which result in the so-called ultradense edge computing (UDEC). Task offloading as an effective solution offers low latency and flexible computation for mobile users in the UDEC network. However, the limited computing resources at the edge clouds and the dynamic demands of mobile users make it challenging to schedule computing requests to appropriate edge clouds. To this end, we first formulate the transmitting power allocation (PA) problem for mobile users to minimize energy consumption. Using the quasiconvex technique, we address the PA problem and present a noncooperative game model based on subgradient (NCGG). Then, we model the problem of joint request offloading and resource scheduling (JRORS) as a mixed-integer nonlinear program to minimize the response delay of requests. The JRORS problem can be divided into two problems, namely, the request offloading (RO) problem and the computing resource scheduling (RS) problem. Therefore, we analyze the JRORS problem as a double decision-making problem and propose a multiple-objective optimization algorithm based on i-NSGA-II, referred to as MO-NSGA. The simulation results show that NCGG can save the transmitting energy consumption and has a good convergence property, and MO-NSGA outperforms the existing approaches in terms of response rate and can maintain a good performance in a dynamic UDEC network.