I'm not a lawyer or giving legal advice on a course of action, only explaining my understanding of relevant law and licensing.
There are two things here: copyright and licensing. They cannot be mixed up if you want a clear picture of what's permitted. Because each use completely different rules, they can have different, even opposite answers! Therefore you first have to determine which have control over what you wish to do.
What the OGL is a license for is to re-use the text that it is licensing. You're not aiming to do that, so the OGL is entirely irrelevant to your purpose. Even if you could adjust your purpose to somehow use the license (and were willing, as it requires, to print the OGL verbatim and legibly on every T-shirt and mug!), it indicates in clause 1.e that characters and their names and likenesses are Product Identity by default.
So, yes, the Greyhawk pantheon happens to be Product Identity, but that's irrelevant (i.e., can't stop you) because the OGL doesn't control the use you're aiming for anyway. So what does copyright have to say?
It is unfortunately straightforward in this instance. Copyright grants monopoly rights over particular expressions of ideas. The deities of Greyhawk are original creations and therefore are protected by copyright. That means that Wizards of the Coast has a monopoly on publishing their likeness in all media, including T-shirts, until the term length of their copyright expires.*
So basically: no, you can't use them in any way.
* Due to repeated extensions of copyright term limits by the U.S. Congress and the exporting of those extensions via various international treaties, in most places in the world the copyright won't expire until most of us are dead.