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JavaScript (ES6), 110 104 bytes

Saved 4 bytes thanks to edc65

let f =

_=>`1o
6o
3o
 9
/44\\__
|2J5|1\\
|3A4|1|
|4V3|1|
|5A2|__/
\\9/`.replace(/\d/g,n=>' _'[n>>3].repeat(++n))

console.log(f())

How it works

The compression of the original ASCII art is achieved by replacing all sequences of 2 to 10 consecutive spaces and the two sequences of 10 consecutive underscores with a single digit:

• Each sequence of N consecutive spaces is encoded with the digit N-1.
• The underscore sequences are encoded with a 9.

We use N-1 rather than N so that we never have to use more than one digit. Hence the need for ++n when decoding.

The expression n>>3 (bitwise shift to the right) equals 0 for n = 1 to n = 7 and equals 1 for n = 8 (not used) and n = 9. Therefore, ' _'[n>>3] gives an underscore for 9, and a space for all other encountered values.

The only special case is the sequence of 10 consecutive spaces just above "JAVA". Encoding it with a 9 would conflict with the underscore sequences. So we need to split it into two sequences of 5 spaces, encoded as 44.

Jelly, 67 64 bytes

-2 bytes thanks to Dennis (1. remove redundant ”, and 2. replace transpose and run-length decode, ZŒṙ, with reduce by element repetition, x/.)

“Ñṁ{xGgṭḷVỤɲ8ṿfƬT9Ɱ¹=qṀS“$<(ƇỤ08ØÑḌṃṘX6~cuc8HṗḞ2’Dx/ị“ ¶_/\|JAVo

Try it online!

How?

“...“...’ is a list of two base-250 compressed numbers:

[1021021021332411532617161526181616261916162618163425334, 2117114111551155121131612111415121115141211161312111551]

D converts to decimal to yield two lists of digits:

[[1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 3, 3, 2, 4, 1, 1, 5, 3, 2, 6, 1, 7, 1, 6, 1, 5, 2, 6, 1, 8, 1, 6, 1, 6, 2, 6, 1, 9, 1, 6, 1, 6, 2, 6, 1, 8, 1, 6, 3, 4, 2, 5, 3, 3, 4], [2, 1, 1, 7, 1, 1, 4, 1, 1, 1, 5, 5, 1, 1, 5, 5, 1, 2, 1, 1, 3, 1, 6, 1, 2, 1, 1, 1, 4, 1, 5, 1, 2, 1, 1, 1, 5, 1, 4, 1, 2, 1, 1, 1, 6, 1, 3, 1, 2, 1, 1, 1, 5, 5, 1]]

x/ reduces by element repetition to give one list of digits (repeating the number from the first list by the corresponding value of the other):

[1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 3, 3, 2, 6, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 6, 1, 1, 5, 2, 6, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 6, 1, 1, 6, 2, 6, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 6, 1, 1, 6, 2, 6, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 6, 3, 3, 4, 2, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4]

ị instructs to index into the list of the right, one based and modularly (0 indexes into the rightmost item). The list on the right, ¶_/\|JAVo, is simply the character used in the required order where the pilcrow, ¶, is the same code-point as a linefeed. The closing partner of “ is not required as this is the end of the program:

[' ', ' ', 'o', '\n', ' ', ' ', ' ', ' ', ' ', ' ', ' ', 'o', '\n', ' ', ' ', ' ', ' ', 'o', '\n', ' ', '_', '_', '_', '_', '_', '_', '_', '_', '_', '_', '\n', '/', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', '\\', '_', '_', '\n', '|', ' ', ' ', ' ', 'J', ' ', ' ', ' ', ' ', ' ', ' ', '|', ' ', ' ', '\\', '\n', '|', ' ', ' ', ' ', ' ', 'A', ' ', ' ', ' ', ' ', ' ', '|', ' ', ' ', '|', '\n', '|', ' ', ' ', ' ', ' ', ' ', 'V', ' ', ' ', ' ', ' ', '|', ' ', ' ', '|', '\n', '|', ' ', ' ', ' ', ' ', ' ', ' ', 'A', ' ', ' ', ' ', '|', '_', '_', '/', '\n', '\\', '_', '_', '_', '_', '_', '_', '_', '_', '_', '_', '/']

Jelly performs an implicit print of this list, which, since it contains characters, prints as if it were a string:

  o
       o
    o
 __________
/          \__
|   J      |  \
|    A     |  |
|     V    |  |
|      A   |__/
\__________/

CoffeeScript ES6, 214 180 bytes

r="replace";" 1o0n0 6o0n0 3o0n0 _9n0/0 9b0_1n0|0 2J0 5|0 1b0n0|0 3A 4|0 1|0n0|0 4V0 3|0 1|0n0|0 5A0 2|0_1/0n0b0_9/0"[r](/\d/g,(a,b,c)->c[b-1].repeat(a))[r](/n/g,"\n")[r](/b/g,"\\")

CoffeeScript, 135 bytes with hardcoding

f=()->"""  o
       o
    o
 __________
/          \__
|   J      |  \\
|    A     |  |
|     V    |  |
|      A   |__/
\__________/"""