Word or phrase referring to people who talk with unnecessary styles/gestures

Solution 1:

If these gestures are exaggerated, I'd suggest "flamboyant"; if staged, then "affected."

affected:

• assumed artificially; unnatural; feigned: affected sophistication; an affected British accent.

flamboyant:

• florid; ornate; elaborately styled: flamboyant speeches.

(dictionary.reference.com)

Solution 2:

Perhaps animated is the word you are after.

From Merriam-Webster:

animated

1. endowed with life or the qualities of life : alive
2. full of movement and activity < an animated crowd >
3. full of vigor and spirit : lively < an animated discussion >

Solution 3:

A literal alternative could be gesticulator

gesticulate: Use gestures, especially dramatic ones, instead of speaking or to emphasize one’s words

He describes the fascinating journey along the evolutionary path that ‘converted us from wild gesticulators to smooth talkers.’

(Oxford)

Solution 4:

Compulsive talker: sb who talks in a continuos manner to seek attention
Prattler: sb who talks in a childish manner