I don't know much about the olive oil business, but I would guess that there are thousands of small growers like yourself throughout Italy, France, Greece, etc. What have you got to make your product stand out from the competition?
I just did a quick search for "olive oil" and I found a dozen on-line suppliers. I also know that every grocery shop, delicatessen and supermarket in my town sells a range of olive oils, ranging from basic low-cost products to extra-virgin to "value added" oils (such as garlic-infused).
I'm not saying you shouldn't go ahead with this. But you do need to be able to offer some reason for customers to buy your oil rather than anyone else's. That's what you need to think about before you start worrying about the mechanics of on-line selling.
I also think that Ralph made a good point about selling to local restaurants. If you can brand the product to make it look like a tradtional product of your region, that might help with that.