Odom, 34, won two NBA championships with the Lakers and also played for Dallas Mavericks, Los Angeles Clippers and Miami Heat.
He represented the United States at the 2004 Olympic Games in Athens and the 2010 world championships in Istanbul.
Coached by Italian Sergio Scariolo, Vitoria-based Laboral Kutxa are bottom of their Euroleague Top 16 section with a 1-5 record and ninth in Spain's Liga Endesa.