A Bit of a Pickle

CJam, 63

q{"Slt 1:T;L ]',*'[\+']+ ]',*'(\+')+ [
 0:T; C+"35/T=S/(C#=~}fC

Try it online

Explanation:

q        read the input
{…}fC    for each character C in the input
  "…"    push that long string, containing code to handle various cases
  35/    split it into (two) parts of length 35
  T=     get the T'th part; T is 1 when parsing a string and 0 otherwise
          (T is initially 0 by default)
  S/     split by space into an array of strings
  (      take out the first item (containing special characters to check)
  C#     find the index of C in that string
  =      get the corresponding string from the array
          (when C is not found, # returns -1 which gets the last array item)
  ~      execute that string

Now the long string with various pieces of code. Each part has a few characters to check and then a block for handling each one, and the default case.

First part: Slt 1:T;L ]',*'[\+']+ ]',*'(\+')+ [

Slt      special characters to check
######## first block, corresponding to character 'S'
1:T;     set T=1, causing the next characters to be processed with the 2nd part
L        push an empty string/array, which will be used to collect the string
######## second block, corresponding to character 'l'
]        end array
',*      join with commas
'[\+     prepend a '['
']+      append a ']'
######## third block, corresponding to character 't'
]        end array
',*      join with commas
'(\+     prepend a '('
')+      append a ')'
######## last block, corresponding to other characters (practically, '(' and '.')
[        start array

Second part: (newline) 0:T; C+

newline  special characters to check (only one)
######## first block, corresponding to newline
0:T;     set T=0, switching back to the first part
######## last block, corresponding to any other character (including apostrophe)
C+       append the character to the collecting string

Perl, 149 bytes

I have a bad feeling that this is a poor attempt, but here goes:

$/=$,;$"=",";@s=[];/^\(/?$s[@s]=[]:{$p=/S(.*')/?$1:/l|t/?($l="@{pop@s}")|/l/?"[$l]":"($l)":0,push@{$s[-1]},$p}for<>=~/([(lt]|S.*?\n)/g;print$s[0][0];

The script has to be saved in a file and it takes input from STDIN.

Explanation:

# Set the input record separator to undef so that <> reads all lines at
# once
$/=$,;
# Ensure that elements of lists printed in quotes are separated by commas
$"=",";

# The stack. Initialise the bottom element with an empty array
@s=[];

# Tokens are extracted in the for loop a few lines below. Copied here for
# clarity: Read the entire input and iterate over all valid tokens of the
# pickle language
# for <>=~/([(lt]|S.*?\n)/g;
# the token is a mark - push an empty array to the stack
/^\(/ ? $s[@s]=[]
      # token is a string, push it inside the stack top
      : {$p=/S(.*')/ ? $1
                     # otherwise, remove the top and create list or tuple
                     # from it and push it inside the top element
                     : /l|t/ ? ($l="@{pop@s}") | /l/ ? "[$l]"
                                                     : "($l)"
                             : 0 # dummy value
                             # pushing of the string/list/tuple actually
                             # happens here
                             , push@{$s[-1]},$p} 
# read the entire input at once and iterate over all valid tokens
for <>=~/([(lt]|S.*?\n)/g;

# in the end, the bottom element of the stack will be an array with just one
# element which is the string representation of the object
print$s[0][0];