How do I keep fonts consistent?

Hi, We are using webfonts on our blog & site, but some viewers are not seeing them. Our fonts are sans-serif "Oswald" and "Content"... but on ie, and sometimes on mobile devices especially, they see serif fonts. What do you recommend I do, to keep the fonts as consistent-looking as possible, if people can't get to GoogleFonts, or are for some reason, not seeing what I think I'm creating? Fall-backs? Best method? Thank you so much.