"This is from ..." definitely sounds strange.
In a sentence like, "This is Bob", you can use the word "this" to refer to yourself. But this is really only appropriate when you are connecting "this" to your name or a few other cases where you are identifying yourself, like "This is I" (or as most people incorrectly say it, "This is me"). Otherwise, you should refer to yourself as "I" or "me" or use your name. Don't refer to yourself as "this". If you want to, for example, say that you are the owner of the green car, you would say, "I own the green car", not "This owns the green car." Or you announce yourself by saying, "I am here!", not "This is here!" Etc.
A little thought will show that a special case is required when giving your name. Otherwise, what will you link it to? Saying, "Bob is Bob" is recursive and uninformative. Of course you could say "I am Bob", but in the context of introducing yourself on the phone, you're trying to identify who the caller is rather than just identify yourself.
All that said, if you said, "Hi, this call is from Acme Company ..." I don't think anyone would question it. That is, saying "this call" makes "this" refer to the event rather than to yourself, and thus eliminates the strangeness of the pronoun use.
And regardless of all of that, it's generally considered polite to give your name, like, "This is Bob from Acme Company." Just saying, "This is Acme Company calling" sounds very impersonal.