Our local repeater is severely sabotaged by unknown parties. For example, broadcast radio transmissions are repeated. Other times someone will send a transmission, when a qso is in progress. Local authorities were informed but they apparently are ignoring this.
The first thing to do is to listen on the repeater's input frequency. If you hear the interfering signal on the input frequency, then you're probably dealing with deliberate interference; otherwise, you most likely have a technical problem.
If your problem is deliberate interference, then if I were in your shoes I would absolutely use radio direction finding (RDF) techniques to locate the source of the interfering transmission. I've done a few fox hunts, and the best simple technique technique is to travel around with a directional antenna (a yagi is nice but the antenna doesn't have to be that directional), an attenuator (your body in between the transmitter and your antenna sometimes works well enough for a weak signal), and a radio that ideally has a signal strength meter. An offset attenuator, containing an oscillator running at a few MHz and a mixer, offers better attenuation for this purpose much more cheaply than a typical laboratory attenuator.
Triangulation doesn't seem to work very well for precise location because of reflected signals, at least in the mountainous area where I live; it might work better in flat lands, but I'd think it's still not accurate enough to positively identify the building or vehicle with the antenna. With a directional antenna and a good attenuator, you could walk or drive a loop completely around the suspected location of the transmitter and prove that the transmission comes from inside the looped area.
Document your results thoroughly, hopefully with video, and turn your results over to the relevant government officials, which in the US are the FCC and Official Observers like @ZeissIcon says, and then you'll have done all that you can.
In the U.S., if you can foxhunt the interfering transmitter's location, then you might try sending this information to the ARRL: http://www.arrl.org/amateur-auxiliary
The ARRL has access to lawyers who can send a polite letter informing the source of the potential Federal law violation, and the potential monetary penalties for such. This kind of letter from a lawyer can often get the attention of the RFI source’s operator.
One of my local repeaters has a sound bleed from the (very high power) TV transmission on the same tower, and all the repeaters I use exhibit signal problems and interference that might or might not be intentional. For instance, the same one that has the TV bleed also sometimes (re)transmits a Morse code station ID for another station. My Morse is pretty bad, so I'm not certain what the other ID is, and I can't depend on it to record or concentrate on it.
All of this is just part of using the 2 meter band. The FCC has limited funding and personnel for enforcement on individual repeater interference, and even if they're actively investigating, it sometimes takes years to trace down intentional interference, never mind something accidental.
Best I can suggest is either try to work around it, move to another repeater, or listen carefully for identifying information when the interference occurs and pass that information to your local FCC and Official Observer(s).
To add to some already great answers here, the very first thing you should do is listen on the repeater's input frequency.
Do you hear it then? If not, then drive fairly close to the repeater site. Note that an off-frequency signal that overloads the repeater's receiver might also overload your HT. If that happens, then it would be prudent to attenuate the signal to determine if it suddenly disappears at some point or not.
The best way to do that would be to use a step attenuator between your antenna and transceiver, but it could also be done by gradually covering the antenna with aluminium foil*. Or, you could simply drive a little farther away from the repeater.
If the signal suddenly disappears at some point as the attenuation is gradually increased, then it likely is only a spurious "phantom" signal due to the input preamps overloading, and not malicious QRM.
You can examine those signals using a spectrum analyzer. It could also be a product of two signals mixing. But I'll leave the details of that for someone else to expound upon.
Only after doing this should you proceed to triangulate the interference source, assuming that is feasible.
Make finding the culprit or culprits an ongoing contest with a reward in your club. In other words:
Put a big fat bounty on em! ;-)
Once you've ID'ed them, the rest will be much easier. If your club is unable to find em, add more clubs!
