Gmail is not rendering Font correctly on Emails
Gmail does not work with Google Fonts or any webfont.
Gmail supports a number of web safe fonts. I can't locate the list and don't see Oswald listed. Perhaps it's supported, but not listed. Or perhaps it maps to a similar font.
These are the fonts supported by Gmail:
Stackoverflow wants me to post code before I could post the link of fonts that work in Gmail I maintain on JSFiddle. I felt a list of fonts might be useful in choosing a fallback font. I am not being lazy, look at the link and you'll understand.
For more information on fonts in email, check out the article below.
The problem is: the fonts are rendered perfectly on apple mail, on Gmail only Oswald.
For the first part of this question, apple mail supports web fonts. This is the reason you see it render properly across all apple mail clients.
For the second part (Gmail) would have Oswald in its family font, that is the only reason that I can think off that will render Oswald in your emails.
I've tried to figure out, why 'Merriweather Sans' is not rendered correctly, but no chance.
Gmail still has an issue with web fonts linked to emails and that is the reason 'Merriweather Sans' is not rendered.