Can I, without uploading my entire NAS to the cloud, access my NAS though a cloud based service to access via WiFi ? Since I don't own a router, rather a DSL modem.

You would probably need to set up routing in the computer the modem is attached to. Also, you need the modem's IP address, which if it is dynamic (not a static address) may be a problem. Check with your ISP about this.

What cloud service provides the functionality I want; any ?

How do you generally setup routing, my ISP isn't that knowledgable !

How you do it depends upon your operating system - Windows or Linux. It is time for you to do some research. It isn't too difficult, but in order for data to get to the correct computer this needs to be done. If your modem were attached to a router, this would not be necessary, but since it is attached to your computer, then you need to enable routing on your computer.

Can you recommend a cloud based service or they all are capable of this ?
What if the IP is dynamic, is there a solution available ?