For סברי מרנן ורבנן ורבותי  see this question here:  Source for pairing l&#39;chaim with alcohol?
The key phrase is in the Midrash (מדרש תנחומא פ' פקודי סי' ב') which says: 


  כוס של קדוש או של הבדלה [והוא ירא מסם המות שלא יהיה בכוס], והוא אומר סברי מרנן, ואומר הקהל לחיים
  
  Over Kiddush or Havdalah [if one is afraid of poison in the cup], one says "Savri", and the people respond "L'chaim."


ברשות however, should be said, when you are being a host to a meal, and want to gain the permission of the people gathered to join you.

When does one say סברי or ברשות?
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