If you're having trouble seeing it on the page click on "יומני טאלנא" above.
רי"ם = Reb Yitzchok Menachem Weinberg, today's Tolner Rebbe of Bayit Vegan,
ס.ט. = Saba Tolner, his zeide, the old Tolner Rebbe, Reb Yochonon Twersky,
הב"י = is the Bais Yisrool, of course, Reb Yisroel Alter,
ל"ש = the Lev Simcha, Reb Simcha Bunim Alter,
הגרפ"מ = is the Gaon Reb Pinches Menachem, before he was Rebbe, (after which he was known as the אד"ש, and after his passing as the Pnei Menachem,) which was after 7 Tammuz, 5752, when his brother the Lev Simcha passed away.
מו' ד. ח = Moreini Reb Doniel Chaim, son of the Pnei Menachem
Reb Shaul is the Rosh Yeshiva of Sfas Emes in yerushalayim and a son of the Pnei Menachem,
Reb Aryeh was the Pnei Menachem's son who passed away some 20 years ago after being hiot by a bus. He was a son in law of Rav Menashe Klein.
Other Roshei Teivosen are Shamoshim and Gaboyim. I'll tru and answer more R"T question in the comments if you have any. No guarantees, though.