Can a publically traded company on the OTC exchange issue warrants to
a third party (non-insider) with the stike price set at a significant
discount (e.g. 90%) to the current market price? Or does the strike
price have to be close to the market price at the time of issue? For
example, if the stock is trading at $10 per share, can the company
issue warrants to an outsider with strike price of $1?

Why would it want to?

Financeguy --

Do a Google search for what's called by economists "agency problem." 
It's always possible for management to make biased investment
decisions to push capital one way or another.  A fine example was the
S&L scandal of the 1980s when companies with federally-guaranteed
deposits were allowed under de-regulation to invest in the
most-speculative of investments -- with a guarantee that the
government would bail out any failures.

This is a legal finance question that must have some controls. 
Unfortunately I can't help with a precise answer.

Best regards,

Omnivorous-GA