Is there a way to import a spreadsheet into SharePoint List if you don't have Excel installed locally? Can Office Web Apps or even Google drive sheets be used instead of excel?
Edit: I have Excel online and the excel is on One Drive
As long as you are able to save the document on your computer in any capacity you should be able to then go into your Document Library (or whichever library you wish it to be stored) then select "new document" and then use the existing file option to find the file on your computer.
You can start by creating a custom list, and then adding columns to match what is in your spreadsheet. Then you can use the grid/datasheet view in your SharePoint list (click on "edit" in a normal list view, or use "quick edit" in the ribbon). then just copy and paste from your Excel spreadsheet.
The quick edit view can be a little fussy when it comes to copying and pasting, so I'd recommend starting small and spending a little time experimenting. Start with a simple one column spreadsheet and one column sharepoint list and build up to get a feel for what works and what doesn't.
Pasting in to SharePoint works much better in IE than Chrome/Firefox. Also, it can behave differently depending on whether you select a single cell, or click on the row on the left before pasting too.