How to read files with .xlsx and .xls extension in Azure data factory?

Excel files have a proprietary format and are not simple delimited files. As indicated here, Azure Data Factory does not have a direct option to import Excel files, eg you cannot create a Linked Service to an Excel file and read it easily. Your options are:

1. Export or convert the data as flat files eg before transfer to cloud, as .csv, tab-delimited, pipe-delimited etc are easier to read than Excel files. This is your simplest option although obviously requires a change in process.
2. Try shredding the XML - create a custom task to open the Excel file as XML and extract your data as suggested here.
3. SSIS packages are now supported in Azure Data Factory (with the Execute SSIS package activity) and have better support for Excel files, eg a Connection Manager. So it may be an option to create an SSIS package to deal with the Excel and host it in ADFv2. Warning! I have not tested this, I am only speculating it is possible. Also there is the overhead of creating an Integration Runtime (IR) for running SSIS in ADFv2.
4. Try some other custom activity, eg there is a custom U-SQL Extractor for shredding XML on github here.
5. Try and read the Excel using Databricks, some examples here although spinning up a Spark cluster to read a few Excel files does seem somewhat overkill. This might be a good option if Spark is already in your architecture.

Let us know how you get on.