Shifty
Answer: SENSE

Each clue is actually two interwoven clues that need to be Caesar shifted by different amounts to read out. Each answer is actually two answers: one by reading operations as PEMDAS and Caesar shifting, the other by reading colors as ROYGBIV and Caesar shifting. Add the clue shift to the corresponding answer shift (in answer order, taken mod 26 with A=0 as instructed) to get one "operation" letter and one "color" letter per combined answer:

CombinedAnswer and shiftClue and shiftSum mod 26 and letter
+*((-+
AMPPSAWILLOW22EMMXQVO BZMMWEEPING TREE1814O
+*((-+
GRVGIGALPACA20THTTHS YLSHALK AV AOL SSHTHMAMMAL RELATED TO THE LLAMA1913N
(*-(*-(*-
PMSPMSPMSBYEBYEBYE12ZEKZO TUFNSYNC HIT140A
(*-(*-(*-
IRGYYOIGRCLASSICAL20EMKAU HWJAGV SXLWJ TSJGIMWMUSIC PERIOD AFTER BAROQUE82C
^-(+^*^
ESPAEMEMAXIMUM8FULAYMN PUFOYLARGEST VALUE614O
^-(+^*^
VIIGVIRBOOMBOX6FIOX MNYLYILOUD STEREO612M
/((*/(*(-
DPPMDPMPSCOOLCOLOR25LVEO YB QBOOX BKDROB DRKX BON YB IOVVYGBLUE OR GREEN RATHER THAN RED OR YELLOW1615P
/((*/(*(-
YIRBYBOOVBLUEBERRY3RQH RI PDQB SLFNHG HLJKW GDBV DJRONE OF MANY PICKED EIGHT DAYS AGO230A
/(+^(^
DPAEPESEPTET15DOLRM LC PBSBKGROUP OF SEVEN318S
/(+^(^
BOGGOINASSAU12WUJCNUF IZ NBY VUBUGUMCAPITAL OF THE BAHAMAS618S
^+--^
EASSEYUMMY20MVIP KRJKPVERY TASTY93D
^+--^
YGRYGSALSA20YVGTOYN YGAIK UX JGTIKSPANISH SAUCE OR DANCE2014O
+^((^+^((^
AEPPEAEPPEWALLAWALLA22TOWN IN WASHINGTONTOWN IN WASHINGTON022W
+^((^+^((^
VIGYVVIRGIRECURRENCE22CQN BNLXWM CRVN BXVNCQRWP QJYYNWBTHE SECOND TIME SOMETHING HAPPENS1713N
^-(+//-
ESPADDSMAXILLA8LGGVI ARNSFEVUPPER JAWBONE917R
^-(+//-
ORYVRIRBELIEVE13YMNSP YT GJ YWZJTHINK TO BE TRUE218I
-^-+*^-^^/-
SESAMESEEDSSESAMESEEDS0WIGGIH VUAYF NIJJCHACOMMON BAGEL TOPPING66G
-^-+*^-^^/-
VRBBRBBRYYRMISSISSIPPI17EC CDKDO SX DRO CYEDRUS STATE IN THE SOUTH167H
(^/++/
PEDAADAPOLLO11YJWWC YGV GX HGWLJQGREEK GOD OF POETRY819T
(^/++/
YRIGVIHARPER9HIGXCV EAPNTG DG PJIWDG ATTSTRING PLAYER OR AUTHOR LEE1120U
*^-*/(
MESMDPASGARD14GNLD NE SGD MNQRD FNCRHOME OF THE NORSE GODS115P
*^-*/(
IRYIRGVELVET13CYPD PKLBSMSOFT FABRIC163D
^-(*(/
ESPMPDTHEBES15HSFFL DJUZ TUBUFGREEK CITY STATE2514O
^-(*(/
YOBGOGKANSAS12KI IJQJU YD JXU CYTMUIJUS STATE IN THE MIDWEST1022W
/^((^(+
DEPPEPAHITTITE4DVDSVI FW RE RETZVEK VDGZIVMEMBER OF AN ANCIENT EMPIRE913N
/^((^(+
YIRYYBOBLUBBER3ITMXQ RMFWHALE FAT1417R
^*/-*^^+
EMDSMEEASARGASSO14YKG LARR UL YKGCKKJSEA FULL OF SEAWEED208I
^*/-*^^+
VOVGVIOVATALANTA5FQDDJ GTMSQDRRGREEK HUNTRESS16G
/-((^/
DSPPEDSHEETS15NIDWZQBM OWWOTM XZWLCKB WN SMDQVFAVORITE GOOGLE PRODUCT OF KEVIN187H
/-((^/
IOVVYGYELLOW16ZLTXOAIV ZLILOCOWARDLY COLOR319T

These letters spell out ONACOMPASSDOWNRIGHTUPDOWNRIGHT. Down on a compass is South, or S; right is East, or E, etc., spelling the answer SENSE.