像: like, but not the same. Widely used.

这个人长得很像成龙。
This guy looks like Jackie Chan.

如: similar to 像, but not widely used in speaking as a single word. Usually written or ancient. It can aslo make phrases together with other words.
Phrases with 如: 如此(widely used)/如是(written only)

不如……<怎样(such as 好, 多, etc.)>: not as <adjective, such as good, much, etc.> as ...

我不如你乐观。
I'm not as optimistic as you.

他不如他的哥哥帅。
He is not as handsome as his elder brother.

同 as a single word is seldom used in speaking.

不同：not the same (as); or more generally, not like or be different from

和他兄弟不同，他有种幽默感。
Unlike his brother, he has a good sense of humor.

他摇摇头，因为他的想法与此不同。
He shook his head, for he thought differently.

不一样 is similar to 不同, but more oral and casual.

一样 means to be the same as. Usually in the pattern "和……一样" (be the same as ...).

BTW, if you want to say "A and B are identical", you can use:
1) 一模一样, if A and B are different things;
2) 一回事儿, if A and B are names of the same thing.