You can clean the engine using degreaser then spray with water. But before that, cover the alternator, connectors and other components where water ingress may be a problem with aluminum foil (use the cheap one). You can also clean the underside of the engine.
A 30 weight oil is good for your VQ30 engine. Do not use 20 weight since it's viscosity is too thin and may cause metal-to-metal contact in case of overheat (given the condition of your radiator). A good quality 'dino' oil from Costco (Shell & Chevron?) will do the job. If you have been using 'dino' oil, you can stick to it. Sysnthetic oil has a more uniform molecular structure and thus gives better lubrication and can have extended OCI but at a price.
Verify the radiator leak is really on the radiator and not just on the rubber hose fittings. If the radiator is leaking, you have to replace it. If the rubber hoses are soft, time to replace them too. It's not worth the risk. Aside from getting stranded, you can damage the engine. I have replaced the rad in our 99 I30 due to a crack just below the cap. I was able to get it for <$100, including shipping. Search the internet and make comparison check before you buy the radiator. You can do it if you have basic handtools. Just make sure you 'burp' it to ensure no air bubbles in the system.
Refer to link below, LC-15, for radiator removal and installation.
http://www.nicoclub.com/FSM/i30/1998_I30/lc.pdf