Well a lot of nations were actually colonies, commonwealths etc of the western allies. The middle east was being admistered by the british and they were dealing with rebellions against the british siding with the nazi's out of conveincnce.

Anyway one reason was because it was a way to gain national prestige and a voice with western powers after the war ended and they started making treaties. By fighting you secured your right to have a vote, even if it was a small one, or favorable treaties.

Another reason was trade. The blockades of the nation made many nations have to abandon trade with them, and make deals with the allies.

At that point it probably seemed like the war was going to be over for certain after america jumped in and the uk went all in. So it may have seemed like an opportune time to gain some leverage with them.

Many of the nations only sent a few thousands troops to fight over seas, nothing like the commitment of the UK and United states in manpower and materials. Like during world war 1, japan sent ground forces to FRANCE to fight for the allies.

Weapons testing. Some nations may have thought it was a good way to shake down their armies with little overall threat to them.

Without going into the in depth history of each nation its hard to answer them. The middle east in particular was an active theatre for the british and nazi's with its own history.

My advice would be to research each nation independently if you really are curious.

Additionally, as Iran was a client state of the British, why didn't they join the war when Britain did?

Iran was not a client state of the British, even though they had many imperialist ambitions for our country back then. During this period of time the Pahlavi dynasty was the ruling house and Iran declared itself neutral very quickly to avoid any problems. Despite our declaration, we were invaded by the British and the Russians in 1941 from multiple fronts in a surprise attack. In the end, the invading powers forced our leader (Reza Shah) to abdicate and his son, Mohammad Reza Shah Pahlavi, became the king in 1941. In September 1943, Iran declared war on Germany. I don't think the Shah had any other options to pick from considering that the Allied powers had basically forced Iran to their side.

Can I clarify your question please? Are you asking on the assumption that these countries joined the allies immediately after the attack on Pearl Harbour? Because that isn't correct - most of them joined later. Argentina, for example, joined the Allies on 27 March 1945, when the Red Army were less than 50 miles from Berlin, and Chile joined so late that they only declared war on Japan.