Realistic emotional voice conversion (EVC) aims to enhance emotional diversity of converted audios, making the synthesized voices more authentic and natural. To this end, we propose Emotional Intensity-aware Network (EINet), dynamically adjusting intonation and rhythm by incorporating controllable emotional intensity. To better capture nuances in emotional intensity, we go beyond mere distance measurements among acoustic features. Instead, an emotion evaluator is utilized to precisely quantify speaker's emotional state. By employing an intensity mapper, intensity pseudo-labels are obtained to bridge the gap between emotional speech intensity modeling and run-time conversion. To ensure high speech quality while retaining controllability, an emotion renderer is used for combining linguistic features smoothly with manipulated emotional features at frame level. Furthermore, we employ a duration predictor to facilitate adaptive prediction of rhythm changes condition on specifying intensity value. Experimental results show EINet's superior performance in naturalness and diversity of emotional expression compared to state-of-the-art EVC methods.