The current (and past) GTVA forces in the Solar theater consist of elements of the 2nd, 4th, and 5th Terran fleets, and of those fleets, portions of the 2nd, 13th, 14th, 15th, and 16th Terran Battlegroups.  Keep in mind that this is not and at this point CANNOT be a full list of all GTVA ships in Sol, only what I could glean from briefings, mission events, and the fiction.  Only one ship on this list (the GTCv Harpy) is actually left unnamed in the fiction, and I took the liberty of naming it myself since it has been confirmed in theater, but remained nameless.
GTVA Solar theater OrBat:
2nd Fleet, consisting of the Terran 2nd (provisional designation) and __th Battlegroups
2nd  Battlegroup:
Flagship - 
   GTD Carthage, Orion class destroyer.  Remains in theater.  Recently participated in destruction of majority of Wargods battlegroup.  CO:  Admiral Anita Lopez.
Supporting warships -
   GTCv Leander, Deimos class corvette.  Destroyed or driven off by Wargods.
   GTCv Iolanthe, Deimos class corvette.  Destroyed or driven off by Wargods.
   GTCv Deianira, Deimos class corvette.  Destroyed or driven off by Wargods.
   GTCv Legionary, Deimos class corvette.  Destroyed or driven off by Wargods.
   GTCv Arethusa, Deimos class corvette.  Destroyed by Wargods and supporting Narayana frigate.
   GTCv Atenor, Deimos class corvette. Captured by Wargods.
   GTC Norfolk, Aeolus class cruiser.  Captured by Wargods.
   GTC Voronezh, Aeolus class cruiser.  Destroyed or driven off by Wargods.
   GTC Joketsu, Aeolus class cruiser.  Destroyed or driven off by Wargods.
   GTC Grissom, Leviathan class cruiser.  Destroyed or driven off by Wargods.
   GTC Systema, Leviathan class cruiser.  Destroyed or driven off by Wargods.
Supporting fighter squadrons -
   39th Szczerbiec
   61st Kampilan
   63rd Sword-and-Spear
   161st Yoshisada
   181st Bloodhounds
   202nd Lobos
   330th Scythians
   332nd Firebearers
   378th Blue Diamonds
   380th Executioners
   401st Ninetails
   402nd Tulwar
   491st Balrog
   507th Goliaths
   529th Kilji
   663rd Firebearers
4th Fleet, consisting of the Terran 13th and 16th Battlegroups.
13th Battlegroup:
Flagship - 
   GTD Meridian, Hecate class destroyer.  Forced to withdraw from Sol after engagement with UEF 2nd Fleet, First Frigate Division and supporting elements.  CO: Admiral Cyrus Severanti
   GTD Hood, Hecate class destroyer.  CO: Unknown  
Supporting warships - 
   GTCv Juarez, Deimos class corvette.  Destroyed or forced to withdraw by 2nd Fleet, First Frigate Division and supporting elements.
   GTCv Harpy, Deimos class corvette.  Destroyed during the First Battle of Neptune.     
   GTCv Cardinal, Deimos class corvette.  Driven off after taking heavy damage.
   GTCv Indomeneus, Deimos class corvette.  Remains in theater.
   GTCv Regensburn, Deimos class corvette.  Driven off after taking heavy damage.
   GTCv Redoubtable, Deimos class corvette.  Forced to withdraw after taking heavy damage.     
   GTC Essex, Aeolus class cruiser.  Destroyed or forced to withdraw by 2nd Fleet, First Frigate Division and supporting elements.
   GTC Ajax, Aeolus class cruiser.  Destroyed or forced to withdraw by 2nd Fleet, First Frigate Division and supporting elements.
   GTC Cho, Aeolus class cruiser.  Remains in theater.
   GTA Argus, Charybdis class support vessel.  Remains in theater.
Supporting fighter squadrons -
   9th Fighting Tarsiers
   11th Tactical Assault (name forthcoming?)
   42nd Pythons
   42nd Striders
   66th Scarlet Horse
   75th Vigilantes
   77th Tactical Strike (name forthcoming?)
   101st Sidewinders
   103rd Archers
   500th Helldivers
   500th Gladiators
   545th KukGris
   508th Prowling Bears
   555th Swordfish
   556th Stallions
   591st Flare Riders   
   899th Undine
16th Battlegroup:
Flagship(s) - 
   GTD Requiem, Hecate class destroyer.  Nominal flagship of the battle group, forced to withdraw after an ambush by 3rd Fleet.  CO: Unknown
Supporting warships - 
   GTCv Arcane, Diomedes class corvette.  Detached to SOC service.  Remains in theater.   
Supporting fighters squadrons -
   93rd Adders
   315th Jade Falcons
   501st Legionnaires
5th Fleet (provisional designation), consisting of the Terran 15th and 14th Battegroups.
15th Battlegroup:
Flagship - 
   GTD Atreus, Raynor class destroyer.  Currently remains in theater.  CO: Admiral Chiwetel Steele.
   GTD Imperieuse, Titan class destroyer.  Currently remains in theater.  Destroyed the greater portion of the Wargods battlegroup. CO: Rear Admiral Verena Winters
Supporting assets -
   GTCv Siren, Chimera class corvette.  Destroyed by Wargods battle group.
   GTCv Hydra, Chimera class corvette.  Part of Serkr team.  Remains in theater.
   GTCv Pilum, Chimera class corvette.  Part of Serkr team.  Remains in theater.
   GTCv Marcus Glaive, Bellerophon class corvette.  Part of Serkr team.  Remains in theater.
   GTCv Medea, Diomedes class corvette.  Destroyed by the Wargods battle group.
   GTCv Valerie, Diomedes class corvette.  Destroyed by UEFg Indus.
   GTCv Triteia, Diomedes class corvette.  Escapes destruction at the hands of the UEFg Katana and Altan Orde.
   GTCv Ania, Deimos class corvette.  Destroyed by the UEFg Katana and Altan Orde.
   GTCv Thalassa, Deimos class corvette.  Destroyed by the UEFg Katana and Altan Orde.
   GTCv Snipes, Deimos class corvette.  Remains in theater.
   GTC Courageous, Hyperion class cruiser.  Remains in theater.
   GTC Novikov, Hyperion class cruiser.  Remains in theater.
   GTC Elissa, Hyperion class cruiser.  Remains in theater.
   GTC Utica, Hyperion class cruiser.  Destroyed by Wargods battlegroup.
   GTL Agincourt, Anemoi class logistics ship.  Captured by Wargods.
Supporting fighter squadrons -
   2nd Stormriders
   11th Strategic Assault (name forthcoming?)
   12th Tactical Bomb (name forthcoming?)
   13th Strategic Assault
   41st Bengals
   60th Bloodletters
   119th Immortals
   212th Silver Scythes
   465th Illusionists
   744th ESMS 'Avalanche'
   908th Trailblazers
   909th Stingrays
14th Battlegroup:
Flagship - 
   GTD Orestes, Raynor class destroyer.  Departed Sol theater hours after commencement of hostilities.  CO: Admiral _____ Morian
   GTD Temeraire, Titan class destroyer.  Departed Sol theater hours after commencement of hostilities.  CO: Rear Admiral Thea Carey
Supporting assets - 
   GTCv Boreas, Bellerophon class corvette.  Departed Sol theater hours after commencement of hostilities.
   GTCv Labouchere, Chimera class corvette.  Defected to the UEF.
   GTCv Miranda, Chimera class corvette.  Departed Sol theater hours after commencement of hostilities.
   GTC Bretonia, Hyperion class cruiser.  Departed Sol theater hours after commencement of hostilities.
   GTC Duke, Hyperion class cruiser.  Defected to UEF.
   GTC Persephone, Hyperion class cruiser.  Departed Sol theater hours after commencement of hostilities.
   GTL Solace, Anemoi class logisitics ship.  Defected to UEF. 
   GTL Fortune, Anemoi class logistics ship.  Departed Sol theater hours after commencement of hostilities.
Oh, and before I forget, thanks to Mars, Droid, Hades, and Battuta for helping and pointing out the numerous ships I missed.