Myneni got the better of compatriot Ramkumar Ramanathan 7-5 7-5 in his second round while seventh seed Somdev advanced when his opponent Philipp Petzschner retired.
Somdev was leading 4-1 when the German wild card withdrew due to a shoulder problem.
Myneni now faces Britain's Kyle Edmund while Somdev is up against second seed Japanese Tatsuma Ito.
In the doubles, the Indian pair of Myneni and Sanam Singh reached the semifinals with a hard-fought 6-4 1-6 11-9 win over Jonathan Eysseric from France and American Tennys Sandgren.
However, India's Divij Sharan and his second seed German partner Frank Moser suffered a shock 1-6 1-6 defeat against wild card Taipei pair of Cheng-Peng Hsieh and Chu-Huan Yi to bow out of the hard court tournament.