"Just as one separates oneself from excreta, urine, a foul odor, a corpse and the sight of nakedness for Kri'at Shema, so too, he should separate himself for Shemoneh Esreh". (Rambam. Hilchos Tefillah 4:8 in translation.) One "should wear suitable clothes when he goes to pray, like one who goes before an important minister". (Online translation of Kitzur Shulchan Aruch 12:1.) The Rambam seems to agree. (Hilchos Tefillah 5:5 in translation.)
At hashkafah.com, the user named "critic" asks:
If someone has body odor (BO) and they can't smell themselves, would they be able to make a bracha?
I also wonder: May they say words of Torah?
If I'd gone jogging in mid-morning, and was meeting an important minister in mid-afternoon, I wouldn't just change. I'd also shower: even though I normally don't notice it, jogging does makes me smell. Before saying blessings to the King of Kings, and before discussing His laws, must I shower?
Please cite sources.