Can I export custom data from a Contact, an Organization and an Activity in one export?
There is a very useful extension called "Extended Reports" that has an Activities report that allows you to pull information about the Source, Target and Assigned contacts, but if you are looking for information about an organization that is related to one of those contacts but is not directly linked to the activity (and you don't have access to a developer), then you'd probably be better off searching twice:


Search > Advanced Search
Search 1:


  
  Select "Display Results as" = Activities
  Enter desired search criteria for Activities
  Search and Export search results
  

Search 2:


  
  Without changing the criteria you used to search for the activities, click to expand the Edit Search Criteria bar
  Select "Display Results as" = Related Contacts 
  Select the relevant relationship
  Export results
  

Use a vlookup function to match data accordingly (facilitated if you export contact IDs)


Hope this helps!
Tamar