Syphilis is 6 weeks. A few people may take up to 90 days, but the huge majority will test positive by 6 weeks, and syphilis is uncommon, so unless you know that you've been exposed to syphilis for sure, 6 weeks is fine.
Hepatitis B is the only hep you need to worry about sexually, generally speaking. It can take up to 3 months to show positive on a test. You can ask your doctor for a test to see if you've been vaccinated for it already. If you have, you don't need to worry about this. If you haven't, talk to your doctor about receiving it.
Hep A is found in fecal matter (poop) and is usually transmitted by contaminated water and food. It can sometimes, but is not commonly, be transmitted by unprotected anal sex. There is also a vaccine for this. Most adults with hep A will get symptoms a few weeks after exposure.
Hep C is only found in blood, and is rarely transmitted sexually. When it is, it's usually unprotected anal sex. It's usually transmitted by sharing needles for drug use, or other drug paraphernalia. It can also be transmitted with non-sanitized or used tattoo equipment, including ink. You can test for that at 6 weeks, though it make take as long as 90 days.
Gonorrhea and chlamydia can be tested for at 5 days after exposure.