Her work has been exhibited in various galleries and museums, including at Gallery Z in Providence, Rhode Island, the Armenian Library and Museum of America Contemporary Art Gallery in Watertown, Massachusetts, the Bromfield Gallery in Boston, and the Village Quill in Tribeca. Past series include Bus Stop, which deals with isolation and time; Hopscotch, which investigates the grid in painting and children’s games; and Celestial Pantomimes, which challenges conventions associated with black-and-white contrast and with particular materials such as black velvet and religious trinkets. 

Current and ongoing series include Palimpsests; Cordia Botanica; Parables; Watercolors: Paintboxes; and Shadows of Peacocks. Her painting ‘Lessons From History’, from the Palimpsests series, was shown in the 1st Armenian Women’s Art Exhibition in New York City. 

Her work has been reviewed in Art Slant, Artscope (‘Blasts’), The Providence Journal (‘Best Bets’), Art New England, The Boston Globe, and Armenian Art Magazine (published in Yerevan, Armenia). Two of her paintings from the Shadows of Peacocks series, ‘Exile’ and ‘Habits of Civilization’, have been featured in Studio Visit magazine, vol. 5. 

Odabashian teaches elementary art in the Westwood (Massachusetts) Public School System and has taught drawing courses at the School of the Museum of Fine Arts, Boston. Her most recent solo show, In the Shade of the Peacock: Parables, Paintboxes, and Other Work in Diverse Media, was at the Armenian Library and Museum of America Contemporary Art Gallery from September 13 until October 10, 2009
 Her current work explores themes of identity, pictoriality and iconographic traditions.