I know this thread is 4 months and 1 day old, but as I'm learning things, I see subjects I can learn more from by bouncing ideas off them.
I also don't believe "my God can beat up your God". I like the saying "God(dess) shows [him- her- it-]self in a way meaningful to the believer", i.e. "everyone sees God(dess) in their own way. To that end, my Gods are just as valid as that person's Gods, and vice-versa.
However, I'm of two minds about enshrining certain deities together in the same shrine. For example, I have a picture of Heimdall in my shrine, but I have a picture of Loki elsewhere in the house. I've come to learn that Loki is a very complex character who brings a sort of balance, or brings out the "flavors" and intensifies the personalities of the other Gods. Therefore he is as worthy of veneration as any other deity. But Loki and Heimdall detest each other and will kill each other at Ragnarok, therefore I think it would not be such a good idea, possibly even disrespectful to enshrine them together.
The second part is that certain deities are worshiped, venerated, and made offerings to in different ways. My biggest conflict right now is incorporating certain Hindu deities into my practice. I don't identify as Hindu, I don't practice as a Hindu, I don't hold with 90% of Hindu beliefs, but I still have an affinity for certain Hindu Gods: Lakshmi, Saraswati, Hanuman, Shiva (as Nataraja). Strangely, and departing from 99.99989% of Hindu views, I have never gotten close to Ganesha or Krishna, despite them being two of the most popular deities. Though I'm sure they love me anyway.
I tried to enshrine the Aesir and Hindu Gods together, but it didn't feel right. The Aesir can be offered alcohol and meat (though I don't think it's a requirement); but that is an effront to the Hindu deities. Moreover, the disposition of the offerings are different for the two pantheons. So for now I keep the Hindu deities separately enshrined. And, while I may think of them, I find myself not praying or offering to them. They are kind of just there. Of course this could just be a matter of not cutting ties fully. After all, Frigga is the All-Mother, Thor is my strength and protector. On the other hand, I can probably use all the help I can get.
The point is, I think it's OK to believe in, and venerate and worship deities from disparate pantheons, but one has to know their respective tastes. For example, at a holiday dinner at my house, if one or some of my guests were recovering alcoholics, I would not keep bottles of wine or liquor on the table, but rather, in the kitchen., If someone wanted it, they could go serve themselves. You have to be aware of people's (deities') sensibilities.
Of course, anyone should feel free to point out shortcomings in my thinking, and offer other views.