This is also known as a neutral crush.
As the allies set-up to hit all the neutral territories at roughly the same time.
Spain: First off make sure that your transports are well guarded off Gibraltar (sz91), and keep in mind that if the Italians have transports that they can open up landing spots in Northern Africa for the Germans to air sweep your fleet
Tip: Say you have 8 loaded US transports (16 ground units) coming over. Be patent and station your ground units on Gibraltar (don’t leave them on transports). This will allow those units to walk into Spain for the attack and your transports head back home on the same turn that you attack. You should also have several more transports coming over from DC attacking Spain on the same turn. Now you will have transports coming and going every turn (this is known as a shuck-shuck).
You also need to have the UK ready to bring in more ground units if possible, and land as many UK fighters as you can to boost up your defense. Would be a good idea to have both the US/UK bring in some AA guns too.
Turkey: This is tricky because the Germans and Italians are well with-in reach. You could have the Russians hit it just before you invade Spain, or the UK right after (or both). You may just hit and run to kill off the free units.
Saudi is a good target for UK from Egypt, and you should be able to get the other two African neutrals at some point.
Afghanistan is a good target for the UK PAC, but will weaken India. Some games I have found it ok to withdraw from India to bolster the Middle East or Russia though. You can plan it to look as if you are evacuating India because of pressure form Japan, and move your units to West India, then hit Afghanistan to get off the coast.
South America: I have had the Anz set-up to hit the South American neutrals. They are really in a good position to do so and the income is better for them IMO (probably still have the US take Brazil for the units).
So all you are leaving is Sweden and Switz, not to bad.