West Brom attacker Odemwingie last featured for Nigeria in a Nations Cup qualifier in Rwanda in February, while Martins, now playing for Levante in Spain, failed to impress in a recent friendly in Venezuela.
Danny Shittu, who has been in superb form for his English second-tier side Millwall this season, has been recalled after last playing an international match at the 2010 FIFA World Cup™.
The 32-man provisional Nigeria squad has two uncapped overseas youngsters in Rabiu Ibrahim from Celtic and Kenneth Omeruo, who features for Dutch club ADO Den Haag on loan from Chelsea.
Keshi, who will take his players to Faro, Portugal, for a training camp from 27 December, must reduce the squad to 23 by 9 January.
The Africa Cup of Nations gets underway on 19 January.
Goalkeepers: Vincent Enyeama (Maccabi Tel Aviv/Israel), Austin Ejide (Hapoel Be'er Sheba/Israel), Chigozie Agbim (Enugu Rangers), Daniel Akpeyi (Heartland)
Defenders: Elderson Echiejile (Braga/Portugal), Juwon Oshaniwa (Ashdod FC/Israel), Benjamin Francis (Heartland), Joseph Yobo (Fenerbahce/Turkey), Efe Ambrose (Celtic/Scotland), Solomon Kwambe (Sunshine Stars), Azubuike Egwuekwe (Warri Wolves), Danny Shittu (Millwall/England), Kenneth Omeruo (ADO Den Haag/Netherlands), Godfrey Oboabona (Sunshine Stars)
Midfielders: Mikel Obi (Chelsea/England), Nosa Igiebor (Real Betis/Spain), Ogenyi Onazi (Lazio/Italy), Raheem Lawal (Adana Demirspor/Turkey), Obiora Nwankwo (Padova/Italy), Fegor Ogude (Valerenga/Norway), Gabriel Reuben (Kano Pillars), Rabiu Ibrahim (Celtic/Scotland)
Forwards: Ahmed Musa (CSKA Moscow/Russia), Emmanuel Emenike (Spartak Moscow/Russia), Brown Ideye (Dynamo Kiev/Ukraine), Victor Moses (Chelsea/England), Uche Kalu (Rizespor/Turkey), Bright Dike (Portland Timbers/ USA), Shola Ameobi (Newcastle/England), Ikechukwu Uche (Villarreal/Spain), Ejike Uzoenyi, Sunday Mba (Enugu Rangers)