Shaking is often a sign of pain and or weakness (neurologic) in dogs. Either of these or both fit with his back side appearing crooked and improvement with exercise/movement. Muscular skeletal pain is very common in older dogs. Spinal arthritis and intervertebral disc problems are also common.
There are other causes of shaking in older dogs. The best bet on getting an accurate diagnosis and treatment is to have your dog checked by his vet.
Diazepam (Valium) is a good drug for anxiety and useful in stopping seizures. It does not sound like either is the problem in your dog's case. It is not useful for pain, weakness or neurologic problems.
Empirically treating pain and inflammation (arthritis) would be a reasonable way to help diagnose if pain is involved and as treatment for pain. Non-steroidal antiinflamatory drugs (NSAIDs) are generally effective and reasonably safe. The newer NSAIDs labeled for use in dogs are significantly better than human OTC meds. Examples include RIMADYL/NOVOX (carprofen), PREVICOX (firocoxib), DERAMAXX (deracoxib), ETOGESIC (etodolac), METACAM (meloxicam), ZUBRIN (tepoxalin).
Human NSAIDs can be effective, but are not always safe, in dogs. Dosages for dogs and humans are frequently different. I've seen a few dogs die from bleeding gastric ulcers after being given a couple doses of their owners' naproxyn (Aleve). Human OTC NSAIDs include aspirin, ibuprofen (Advil, Motrin), ketoprofen (ORudis KT) and naproxen (Aleve)
Aspirin is the most commonly recommended OTC NSAID in dogs. The commonly referenced aspirin dose in dogs is 5-15 mg/lb 2-3 times a day. I've always seen side effects, usually vomiting, well below the maximum dose and often below the minimum effective dose. A reasonable starting dose for a 30 pound dog is 2 baby/heart smart 81 mg tablets once or twice a day. A 50-100 pound dog could start on a regular strength adult dose (325 mg).
Ibuprofen is sometimes used by owners. An effective dose that has been mentioned is 5 mg/kg/day. Toxicity (gastric ulcers without other clinical signs) have been reported at 8 mg/kg/day. This is not an adequate margin of safety and sensitive dogs are likely to have more severe toxicosis at lower dosages given that drug effects vary within populations.
Ketoprofen is approved in dogs at 1 mg/kg once a day for a maximum of 5 days. 0.25 mg/kg has been recommended for chronic therapy. Side effects are bleeding and kidney/liver failure, which are similar to the other OTC and prescription NSAIDs.
Alleve, as already mentioned, is not safe.
Meloxicam is available by RX in humans and dogs. Acetaminophen (Tylenol) is not a NSAID, but is sold OTC for pain and fever in humans. The usual dog dose cited is 15 mg/Kg (6.8 mg/lb) no more often than q8h. Acute toxicity is generally not seen at dosages under 100 mg/kg/day. It is very toxic in cats and should never be used.
Let me know if you have follow up questions.