Is it obligatory to answer the host's call to prayer, knowing that one is in a state of janabah, and fearing to arouse his suspicion regarding his family if one refuses?

If you become in a state of janabah, you are obligated to perform ghusl to offer the prayer, and wudu is not a permissible substitute for it. However, if you do not find water or fear harm from using it, then perform tayammum. As for abandoning ghusl due to embarrassment, it is not permissible and does not allow for tayammum. Prayer in a state of janabah is a great abomination and is not accepted, based on the Prophet's (peace be upon him) saying: "No prayer is accepted without purification." Its performer may be punished for it in the grave. Your fear of Allah must be greater than your fear of people, and shyness that leads to abandoning obligations is blameworthy.