It's a feminine noun meaning (roughly) "glory", here in the nominative case.
τω Θεώ is in the old dative case, which has died out in spoken Greek but lives on in a handful of phrases.
So this is literally something like "glory to God", with a jussive(?) "(may there) be" (έστω) understood, i.e. "glory be to God".
I'm neither Greek nor English native, but as far as I understand it, the difference is "επιτέλους = finally" as in "It finally stopped raining" (the rain prevented you from doing something, so you were waiting for it to stop and now you're glad).
"τελικά = in the end / finally / eventually" as in "Eventually we decided to stay at home" (we were thinking about it and now we know what we do, but it's not like we were eagerly waiting for it, like in the first example).
Hope this is true.