For that cue to go for $160, it's probably either warped, damaged, or stolen.
When determining the age of a Meucci cue, you generally have three steps to narrow it down with Meucci cues. The first is the logo on the cue. The "block" logo in the pictures was used up until around 1990. The "olive branch" logo from 1990 to present.
For the pre-1985 cues with the block-style Meucci logo, you can then separate them into two groups based on the style of the butt cap. Pre-1980 cues will have the round bumpers.
Then, of the modern flat bumpers, we can narrow it further. If you remove the bumper and measure the width of the portion that inserts into the cue, you can determine if the cue is from between 1980 and 1988 or from 1989 or newer. the 80's bumpers are around 3/4 inch or 0.750. Newer ones are .675.
All the stuff above is "in general terms" and not the rule. With Meucci cues there are MANY exceptions.
Now, that puts your cue somewhere in the 1980-1990 range in terms of age.
The model is going to depend on how well you can date the cue. What you have is a Meucci Originals M-7 cue from the "Meucci Series" from the early 90's. Depending on the year it was made, it may be one of the descendants of the Meucci M-7, but I think it's probably an earlier version of the Meucci M-7 pictured below.
Also see this question where the person had a Meucci 95-12 cue with the same design but with the newer logo. His is probably the Meucci 95-12 or Meucci HOF-2 (a newer version of your Meucci M-7).