Is it wrong to say "very almost"?

You can say

"I very nearly fell over!"

but to say

"I very almost fell over!"

will brand you as very nearly a beginning speaker of English. This is a bit harsh for English learners, since nearly and almost mean almost the same thing. But that's how it goes sometimes.

Consider the relevant definitions of the adverbs, very and almost, from the New Oxford American Dictionary (2nd Edition):

• very — in a high degree
• almost — not quite; very nearly

Now, it is standard to modify one adverb with another. Examples:

• very: He dragged the chair very slowly across the room.
• so: Why must she leave so soon?
• almost: We are almost there.
• too: By the time we got there, we knew we'd come too late.

In your example, however, very and almost modify over. There are certainly several instances in English where two adverbs (modifiers) modify a third. Examples:

• so very: Why must she go so very fast?
• almost too: She hit me almost too hard; I nearly passed out.
• far too: You went far too easy on her.

Some other constructions, especially those containing very and so, could be considered colloquial and not suitable in formal writing:

• so very: That was so very good!
• way too: His speech was way too boring! (Actually informal)

Now, the construction, very almost is probably the most unidiomatic of these informal expressions, especially considering the fact that very is already in the definition of almost:

• I almost fell over.
• I very nearly fell over.
• I very almost fell over. [?]
• I very, very nearly fell over. [Better, but overly informal]

These days, the overuse of very is rightly frowned upon. It is not a bad idea to stay away from very and try to use more descriptive language. Certainly, use very as often as you want, but note that very almost is quite unidiomatic in regular formal and semi-formal usage. It may well be more of a regionalism than anything else.