benjaminfrog
phenomenon known as "wolf tones". Here's how Wikipedia defines it:
A wolf tone, or simply a "wolf", is produced when a played note matches the natural resonating frequency of the body of a musical instrument, producing a sustaining sympathetic artificial overtone that amplifies and expands the frequencies of the original note.
That is indeed the classic definition of a "wolf note" or "wolf tone", originally used in describing a behavior of bowed string instruments. The coupling of the played note to the body resonance of the instrument creates a loud, sometimes wild and hard to control note (if it is not exactly at the frequency of the desired note). Energy provided by bowing quickly and easily dissipates into acoustic energy, hence the wolf note is louder than surrounding notes. Due to the bowing (= contiunous excitation) the wolf tone sustains.
The same phenomenon occurs in plucked instruments as well. But in plucked instruments, the excitation is a momentary impulse (the pluck). The energy of the pluck easily feeds the instrument's natural resonance frequency in a wolf note, it dumps the energy rapidly as before, resulting in a strong note, perhaps somewhat detuned if the natural instrument resonance is not exactly at the frequency of the desired note. This part is no different than above.
But where a plucked instrument differs from a bowed instrument, is once the energy of the pluck and coupled resonance is rapidly dissipated, there is no additional sustaining excitation as is provided by the bow. Because of this, the note rings for a shorter period of time than other notes. The typical perception of this in a guitar type instrument is a note that sounds "thuddy" and "odd" rather than clean and ringing. On guitars this typically occurs around the frequency of the open G string. Play some notes around that area, and you may find one that sounds different than the rest - thuddy and odd in some other way. This is your wolf note. If you're lucky, your instrument will happen to have (or by design in hand-made instruments) a resonance between musical pitches instead of exactly at one, and this well reduce the effect, and the wolf may be far less noticable.
So there's everything you never wanted to know about wolf notes in plucked instruments!
Regarding the OP's question, it's hard to say without hearing the issue, but sometimes weird higher resonances can be caused by strings vibrating behind the nut or between the fretted fret and the nut, or sometimes if a string ball isn't seated properly against the bridge plate, it can vibrate. Also, poorly made nuts and saddles without a good break can cause wierd things to happen, as can something loose in a tuner.