Axis & Allies Developer and Playtester; War of the Ring Editor and Playtester
I'm not sure if you're using the 1st or 2nd edition rules, so I'll answer for both.
So russia can declare war on germany and japan anytime
No. The Soviet Union can declare war on Japan at any time. It can't declare war on Germany (or Italy) until its fourth turn, unless either Germany or Italy declares war on it (under 2nd edition rules, the USSR may also declare war if an Axis power captures London).
Usa cant declare war until 4th turn, but japan can declare war on usa whenever they want
usa cant declare war on germany until 4th turn but germany can declare war on usa whenever
Germany and Japan can declare war on the US whenever they want. The US can't declare war on either of them until the Collect Income phase of its 3rd turn unless one or more of the following happens:
1. An Axis power declares war on it
2. Japan makes an unprovoked declaration of war on UK-ANZAC
3. An Axis power captures London or any territory in North America (2nd edition only)
Uk and ANZAC cant declare war on japan but japan can declare war on uk anac
Any of these powers may declare war on the other at any time.