"Spurious" can only refer to abstract things: for example, 'spurious logic' (reasoning that appears to be logical, but isn't) or 'spurious claims' (claims seem plausible, but aren't ). This word doesn't necessarily mean that people are trying to deceive you: it means that an idea isn't as valid or as reliable as it seems - this is the case of phrases such as 'spurious reasoning'. Do bear in mind that this is quite an academic, high-level word: I'd estimate that half the English native speakers meet in the street would have no idea what this word means, and even fewer would use it. Unless you're a philosophy student, for example, you'll probably never need to use it, either.
"Bogus" is less formal and more practical. It also means false, but it can be used for more concrete situations. For example, a bogus police officer is someone pretending to be a police officer. We use 'bogus' to suggest that someone is deliberately trying to deceive others. It could used either in a formal or casual context.
"Fake" is an everyday word. It is similar in meaning to 'bogus', but more informal and more common. You can certainly have a 'fake designer bag' in the sense that it's counterfeit or a forgery. You can't use 'spurious' in this context.