Are the following sentences correct? Do they all mean the same thing?
She talks so much.
She talks too much.
She talks a lot.
She talks very much.
'She talks so much' and 'She talks a lot' are pretty much interchangeable. They are both simply observations without much judgement.
She talks too much is an observation along with judgement – she ought to talk less.
She talks very much is not a full sentence an AmE speaker is likely to say – don't know about other areas. The only time we're likely to say these words in that order is when followed by a mention of some topic, for example:
She talks very much about saving the children in Uganda.
In OP's context it's probably specious to postulate even a subtle difference in meaning - they all strongly imply that in the speaker's opinion, she talks excessively.
But change the verb to "She loves me..." and most people would interpret only too much as meaning excessively. All the others would be seen as positive statements.
I can't think of any context where so much and very much aren't semantically interchangeable, but the former is definitely more informal.
Some verbs don't seem to work very well with a lot - I'm not keen on "She hates me a lot", for example, but "She argues a lot" seems fine to me.
Note that "She talks very much" is slightly odd, primarily because very much is usually used in "positive" contexts such as "She loves him very much".
TL;DR: There can be differences, but probably not with OP's exact examples.
"a lot" is not proper grammar in that context. A lot is typically used as a measurement of objects. Example: A lot full of cars, or a lot of pallets on the warehouse floor.