Why didn't Yosef, who was extremely strong (as the Midrash describes in Vayigash), grab his cloak from his mistress before fleeing?
Ramban: Out of respect for his mistress.
Oznayim la'Torah: It wasn't from his mistress that Yosef was fleeing but from the Yeitzer ha'Ra. 1
As Chazal said in Avos 1:4
Why does it say "Va'yanas Va'yeitzei" (he fled and went outside)"?
Seforno: Yosef initially fled from the room in order not to be overcome by the Yeitzer ha'Ra. Once outside, he walked, to avoid suspicion that he had done anything wrong.
Hadar Zekenim: "Va'yeitzei" on the merit of "va'Yotzei Oso ha'Chutzah" (Bereishis 15:5-6 - and Avraham believed).
Even though some explain that Yosef needed miraculous help to refrain from sinning (refer to 39:12:3:1 & 2), surely he received the help due to his awesome merits! (PF).
As the Pasuk writes in Tehilim "ha'Yam Ra'ah Va'yanas!" See Oznayim la'Torah as to why the merit extended to the whole of Yisrael.
What stopped Yosef from sinning?
Rashi: The image of his father that appeared to him 1 on the window-sill
Hadar Zekenim (11): It says "Ein Ish" - he checked and found that he has no male organ. Hashem did so to prevent him from sinning.
Why does the Torah add the word "Leimor"?
Peninim mi'Shulchan ha'Gra: When she saw that he refused, she asked him to say "lie with me." This would make him more prone to sin. 1
מכח מה הצליח יוסף לעמוד בניסיון?
מהר"ל (חידושי אגדות ח"ב, עמ' עג ד"ה עתידין, סוטה דף לו:): דמותו של יעקב נראתה לו, ונאמר לו שהוא לא יהיה ראוי להכתב על האפוד אם יחטא, כי בעל זנות הוא חומרי ואין דבר יותר קדוש מהאפוד.