Nowadays, wireless sensor networks (WSNs) are more and more used in applications such as environment monitoring, healthcare monitoring, etc...The challenge in sensor networks is to ensure the sustainability of the system by guaranteeing the required performance level. However, with the limited capacity of finite power sources and the need of guaranteeing a long lifetime of those systems, it is suitable to use energy harvesting which allows to supply low-power electronic systems by converting ambient energy into electric power. Hence, our study is concerned with the problem of soft periodic and aperiodic tasks scheduling in sensor nodes powered by energy harvesters. In this paper, we address this issue by proposing three energy-aware schedulers, namely BG-Green-RTO, BG-Green-BWP and Green-AWP which aim to improve the responsiveness of aperiodic tasks while still guaranteeing the execution of periodic tasks considering their timing and energy constraints. Such algorithms allow to gracefully cope with processing overload and energy starvation. Moreover, a simulation study permits to show their performance.