As a noun, "avail" means benefit or effect. Therefore, if I accomplished some task to no avail, it would mean I was unsuccessful. "The medical responder gave the victim mouth-to-mouth resuscitation, to no avail".

SIMPLY means no luck

It plain text, it means "no end/does not give up". I could say "he tried to open the door by force, but to no avail." (in short, the door stayed shut.) not used as a encouragement. "don't avail!" is heard rarely but it really is not used in. That context in modern speech.

Futile/fruitless