I am not sure if there are any automated ways that would allow you to transfer your data from mysql / Excel to SQL Azure, however, hopefully I can help point you in the right direction to get some of this going yourself.
The first step would be to create a process that will export your data into a common format. Perhaps something like a tab delimited file. There are a ton of examples on the web on how to do this from MySQL and I think something like the OpenXML
SDK or with an OleDbConnection would work to get the data from Excel.
From there you could use the bulk copy utility to load the data from your file into SQL Azure. Here is an example:
I would suggest to use SQL Server Integration Services (SSIS)… it is not a lightweight tool but is the correct tool to use for that purpose. I have used it to transfer data from OnPrem to Azure creating a DTSx package, it can be as simple as just "export"
data or complex if you need to transform some information (or adapt data types). SSIS can manage different data sources as OleDB and Excel.
Then I have deployed the package to an OnPrem SQL Server instance and scheduled the transfers using SQL Server Agent. It is the most robust aproach.