Thalidomide is best remembered for two faces: a notorious teratogen of the past and a useful immunomodulator of the present. We must find the wrong claim.
Begin with the clinical uses. In leprosy, the inflammatory type 2 reaction (ENL) is driven by tumor necrosis factor alpha, and thalidomide brings this cytokine down, so it is a recognised therapy for ENL. That validates option A. Its anti-angiogenic property, blocking new blood vessel growth that tumors need, makes it effective in multiple myeloma for both first-line and relapsed disease, usually paired with steroids. That validates option C.
Now the history. The drug was sold around 1957 as a calming agent and to ease nausea of early pregnancy. When thousands of babies were born with phocomelia, the limb-shortening defect, it was pulled from the market. That validates option B.
Finally the side-effect profile. Typical complaints are drowsiness, constipation, tingling neuropathy and a real risk of clots in the veins, plus its severe damage to the unborn child. It does not characteristically cause loose stools, nor does it produce a euphoric high. Therefore the statement that its commonest effects are diarrhea and euphoria is simply untrue.
$\therefore$ The false statement is the one about diarrhea and euphoria.
\[\boxed{\text{Most common side effects are diarrhea and euphoria}}\]