According to Oxford Advanced Learner's Dictionary in the entry “know” and thefreedictionary.com, “How should I know?” means “I don't know and I am not the person you should ask” or “I do not know.; Why should I be expected to know?” respectively. My question is that what is the meaning of “How I know” compared with “How should I know”? Google returns more result for “How I know?” than “How should I know”.
Context is everything. How I know can be used in several grammatical ways, but not as a question.
Questions that start with interrogative words take an auxiliary verb in contemporary English unless the interrogative word is the subject, as in Who said? or What happened yesterday? Here, how is not the subject; it is a pro-adverb rather than a pronoun, asking in what manner? or to what extent? As such, it takes an auxiliary verb:
- How do I know?
- How can I know?
- How would I know?
- How might I know?
and so on. You have identified the usual meanings of how should I know.
If how is not being used to introduce a question, it is grammatically valid in several other cases.
How I know may be a subordinate clause:
The children have stopped singing along to the movie. That's how I know they're tired.
How can be used to intensify, though I would say it is not common nowadays in speech:
I must be blunt. Your partner is cheating on you.
Yes, I know. How I know!
If how is a noun, referring the method or manner in which something is done, I could read it as an inverted sentence, if a comma is present:
Do you know how to fix my phone?
How, I know. When I'll have time is another story.
Web search results are not the best way to judge relative usage. How I Know appears to be the title of a popular song, for example, and is thus overrepresented compared to other writing or speech. Google ignores punctuation, which can make a big difference in meaning, and its results furthermore vary from region to region and over time as its index and algorithms change. And of course, Google will contain examples of typographic or other errors that should be discounted. Meta.EL&U has a list of corpora among its references which are more reliable.