In my 365 projects, I created a folder called "Modules" inside the "Modules" folder I created another folder called "Scripts", "Images" and "Css", and I put my files in theses folder.
You can create a class what inherits a WebPart and create an override method for OnInit. From there you can create a new literal control
WebUrl is a property with the url of your site.
Don't forget to inherit it in your webpart within the class you created!
I did some research and found this answer: http://joelblogs.co.uk/2011/06/30/embedding-resources-in-sandbox-solutions/
This works for all my files, except the resource files...Not sure how I would do those
This article is about localization in Sandbox, but it shows the method to access the resource files properly.
I use Style library and make a folder for every category like images,scripts,styles