Avoiding nightshade vegetables - no clinical evidence for this myth. Some individuals may find a particular food makes them better or worse but vegetables from the nighshade family are packed full of anti-inflammatory anti-oxidants, phytochemicals and vitamins so cutting them out of your diet means you are missing out on their nutritional benefits.
Gin-soaked raisins, cider-vinegar etc - no evidence from any clinical trials. I'm afraid this one is all anecdote. Not going to do you any harm if you like eating your raisins with gin but it's probably only the alcohol relieving the pain!
Cutting out wheat - I've posted more extensively about this here. In a nutshell, probably not but it depends on what type of arthritis you have.
No starch/London diet/AS diet - one study has been conducted using this diet which did show positive results but it was with only a few patients and the benefits of cutting out starch haven't been found by other researchers. It's a very restrictive diet so definitely not one to try without discussing it with a dietician or doctor first.
Vegan diet - there is some evidence in favour of this for reducing symptoms in inflammatory arthritis based on a series of trials done by a Scandinavian research group. However, no-one else has replicated their results and a Cochrane Review suggested that patients on the diet actually were risking malnutrition in the long term as they weren't well-equipped to ensure they were eating a balance diet. It could be that the weight loss the patients on the vegan diet experienced actually helped reduce inflammation or possibly the diet itself. A vegan diet can be very healthy if its well-balanced so there is no reason to avoid one because of arthritis but probably no reason to choose to go vegan just for your arthritis either.
Diet does have a role in managing arthritis. Being a healthy weight and eating a balanced diet can help reduce some symptoms and improve your overall health. You can find my run down of how to have a healthy arthritis diet here.
Let me know your least favourite diet myths or whether you are actually a secret fan of gin-soaked raisins and emu oil salad dressings!