Assuming you're asking about the US, since you mentioned IRS. Rules may be different elsewhere. That said:
The answer used to be yes. A friend of mine once cashed a check written on a portable blackboard. However the bank manager did tell him that if he wasted their time again with this nonsense they were likely to tell him to close his account.
However, since then the banking industry had gotten rules put in place which effectively forbid this, since they require that the check be able to go through automated scanning systems. I believe they also still require magnetic ink for the routing and check number, which is something most folks would be unable to provide even given the ability to print a visually compliant check.
(In exchange for getting that rule approved, the banks promised to clear checks more rapidly. You often used to have to wait 7-10 business days for the funds to hit your account after the bank received the check; I'm not sure what the official rule is but the norm is now closer to three days.)
Sorry, but "the shirt off my back" is no longer a valid protest payment in the US.