I think you are confused about a few things, which is understandable for somebody new to the tool.
Jira is the software you are using and Greenhopper is an external company that produces plugins for it, mainly the Agile plugin. Components are within Jira and they are simply a way you can categorize your issues. I suggest you find a tutorial video on jira to introduce you better to the tool.
Now, again, these are just tools. They don't dictate how you should work. Jira is very flexible that way so you can do Agile, Scrum, Kanban or whatever methodology you want within it.
You need to first decide what methodology/process you will adopt. Basically, how will you guys work?
Are all the teams working in sprints? Do they have the same deadlines? Are the stories-issues parts of a whole or can each team deliver a full feature on it's own?
For example, if one team is infrastructure, one is UI and one is DB, their parts will likely come together to make a "whole" feature, that is complete and tested.
Another example is if team A is doing a Reporting Module and team B is doing a Login module, their features aren't usually related and they can work separately.
So basically, you can't ask anybody here to give you the straight answer. Stop focusing on the tool and understand how you will work and what makes sense for you.
And remember: agile is trial and error. Try something and if it doesn't work, adapt.