Declaring a variable as volatile means that modifying its value immediately affects the actual memory storage for the variable. The compiler cannot optimize away any references made to the variable. This guarantees that when one thread modifies the variable, all other threads see the new value immediately. (This is not necessarily true of non-volatile variables.)
Declaring an atomic variable guarantees that operations made on the variable occur in an atomic fashion, i.e., that all of the substeps of the operation are completed within the thread they are executed and are not interrupted by other threads. For example, an increment-and-test operation requires the variable to be incremented and then compared to another value; an atomic operation guarantees that both of these steps will be completed as if they were a single indivisible/uninterruptible operation.
Synchronizing all accesses to a variable allows only a single thread at a time to access the variable, and forces all other threads to wait for that accessing thread to release its access to the variable.
Synchronized access is similar to atomic access, but the atomic operations are generally implemented at a lower level of programming. Also, it is entirely possible to synchronize only some accesses to a variable and allow other accesses to be unsynchronized (e.g., synchronize all writes to a variable but none of the reads from it).
Atomicity, synchronization, and volatility are independent attributes, but are typically used in combination to enforce proper thread cooperation for accessing variables.