Large language models (LLMs) can generate fluent dialogue, but prior works lack situational grounding, dynamic strategy control, and evaluation aligned with clinical standards in motivational interviewing (MI). We introduce StoryMI, a multi-LLM agent framework for controllable MI dialogue generation, where questionnaire-based client profiles are expanded into situational stories that provide narrative context for the dialogue. Therapist and client agents generate MI-coded utterances guided by MI codes selected by the interaction agent, while an interaction agent dynamically coordinates exchanges to control MI strategies during a multi-turn conversation. We propose a two-level evaluation protocol: lexical metrics and MI-specific measures of macro-level counseling strategies, alongside LLM-as-judge and human expert assessments. We construct a dataset of 6K simulated MI dialogues grounded in 1K questionnaire-story pairs, covering 12 MI codes and 13 symptom domains, and benchmark six open- and closed-source LLMs. Our results show that situational grounding and macro-level control can improve MI adherence and clinical plausibility, demonstrating the effectiveness of a structured multi-agent workflow for psychotherapy dialogue generation. We provide code and data for reproducibility.