When should one use 报告 (bàogào) or 演讲 (yǎnjiǎng) when saying "to give a talk"?
报告 means "report" 

演讲 means "speech"

It all depends on the content of your speech. 


If you are reading a report to inform people about some facts, you should use  发表报告 (give a report)
If you are invited to educate people in the conference about some facts, then you can use  发表演讲 (give a speech/lecture)
If you are expressing your opinions in the conference,  then you should say  发表言论 (give my opinions/ comments)
In any case, 报告, 演讲 and 言论 are all spoken words, so all can be referred to  "talk" in English " e.g. "who listened to my talk in the conference?"