There were two things related to the problem, try Solution-1 and if you still don't see the actions then Solution-2 should do it (as was the case with me).
1 - Add "New Task/Event/Email" buttons to the object Page layouts
- View the page layout for the object you want to update. Make sure buttons for New Task, New Event, Log a Call, and Send an Email (not Send Email) are added to the Salesforce Mobile and Lightning Experience Actions section of the page layout.
- Make sure your users have permission to create new tasks and events, log calls, and send email.
2- Edit Change global actions
- In the Lightning Experience, Setup Home | User Interface | Global Actions | Global Actions
- Click Edit next to any of the missing global actions (New Event, New Task, Log a Call)
- Look at the 'Record Type' pick list and select any value but --Master--
Note: Solution-1 didn't work because I had multiple record-types for activities.
Above solution is valid not only valid for Lightning-for-Gmail but also for LEX users.
