I want to know if I can run a SaaS service based on Odoo open source code? If true, can I rebrand it? I will be providing infrastructure and support (pretty much like what Odoo.com does) so how legal would that be (with references please if possible). Thanks.
While this topic is very broad and has a lot to consider I will try to give you some insights.
There shouldn't be any legal problem for you to create a SaaS for Odoo. Odoo is open sourced and so you have the right to do anything with the code as you wish, including redistributing. The only thing that I am not 100% sure of is if you can remove everything about the brand and everything that links to Odoo. I would honestly drop an e-mail to firstname.lastname@example.org for this, I'm sure they'll give you feedback on this situation. I know Odoo does ask you to be a partner in order to sell and redistribute Odoo so you might want to become a partner from them too, if you aren't yet. Last but not least will be the changes for Odoo V9. When Odoo V9 will be published there will be quite some changes in licensing (see my other topic about this here). A part of Odoo will become an enterprise edition and in order for you to be able to sell and supply this to your customers you will have to be a partner or you will not even have access to this part of the code. So that might be something for you to consider too.
Have you also thought about the technical side of the story? Creating a SaaS solution isn't too easy and you will need to think about a lot. For example: DNS, firewall, port forwarding, updating Odoo's, support, ability for the customer(s) to add custom code, port forwarding, HTTPS, security, ....
I hope this gives you some sort of insight and answers your questions. If you want to discuss this further or have more questions just reply on this and I'll try to answer them as best as I can.
short answer is yes you can .... provided you respect the licence.
With Odoo V8, you must indicate to all your saas users where to download the code you have modified.
With Odoo V9-Community, you don't have to provide the download link, but if you distribute/sell the new code it must be LGPL or AGPL or GPL and shipped with the code included. If you don't distribute the code, then you can run it for your business as a proprietary software and never divulgate it.
I do provide large scale hosting for Odoo,even for free, and there is no requirement to be a partner if you are not interested in the proprietary part of Odoo V9. You might be a partner for other reasons of course, but the funny fact is that you would be asked to sign a paper in which you commit to promote Odoo Saas and Odoo enterprise "every time it can fit", which would not be consistent at all with your target ;-)