What is the source for R' Meir and R' Elazar being members of Beth Shammai? Also, what is the source for the Beth Hillel membership of R' Yehuda? I heard from several persons (including one Rabbi) they were members of these Academies but I do not have the source for this information.
Re: R' Eliezer, In Niddah 7b it says:
כל ימיו של רבי אליעזר היו עושין כרבי יהושע לאחר פטירתו של רבי אליעזר החזיר רבי יהושע את הדבר ליושנו כרבי אליעזר בחייו מ"ט לא משום דרבי אליעזר שמותי הוא
(Note the word in bold: שמותי)
The generally accepted translation in English is:
Throughout the lifetime of R. Eliezer the people acted in accordance with the ruling of R. Joshua, but after the passing away of R. Eliezer, R. Joshua re-introduced the earlier practice. Why did he22 not follow R. Eliezer during his lifetime? — Because R. Eliezer was a disciple of Shammai
Note that the key is the word שמותי. Rabeinu Tam and the Rashba translate it as "disciple of Shammai" (proof being that R. Eliezer frequently/always sides with Beit Shammai). Rashi notably translates it as "being under the ban" (reference to the story of the "tanur shel achnai").
Re: R' Meir, R' Yehuda:
I don't currently have as good a source for these two, but here is some circumstantial evidemce:
1) Rabbi Akiva has a dispute with someone from Beit Shammai (and apparently gets totally creamed in a logical argument) in Yevamot 16a (אתה הוא עקיבא ששמך הולך מסוף העולם ועד סופו אשריך שזכית לשם ועדיין לא הגעת לרועי בקר). This implies that Rabbi Akiva is a Beit-Hillel kind of guy.
2) Pretty much all of mishna is the students of R' Akiva, (he's basically the only one who gave smicha after the Romans prohibited it) -- R' Yehuda, R' Shimon, R' Meir, R' Yossi, and R' Nechemia. This implies that R' Yehuda and the others would technically be Beit Hillel.
3) The exception is R' Meir, who was also a student of R' Yishmael. There are a bunch of "ifs" going on here, because it appears that "Meir" was a nickname so we don't really know who he was. Also, there is likely more than one R' Yishmael (one of which was Kohen Gadol), so things are a bit murky. In any case, there are halachot in the names of R' Yishmael and R' Meir that are both in agreement with Beit Shammai.
Chagiga 6a (brought in the other answer by Danny) has R' Yishmael and R' Eliezer in agreement with B' Shammai
Nazir 9a has a Beit Shammai halacha that shows agreement with R' Meir.
The Gemara in Chagiga on the bottom of 6a - top of 6b mentions that Rav Elazar holds (in a certain historical case) like Bet Shammai.
That doesn't mean he was a member of Bet Shammai, but in this case he held against Bet Hillel.
אמר אביי: "בית שמאי, ורבי אלעזר, ור' ישמעאל, כולהו סבירא להו עולה שהקריבו ישראל במדבר עולת ראייה הואי. ובית הלל, ורבי עקיבא, ור' יוסי הגלילי, כולהו סבירא להו עולה שהקריבו ישראל במדבר עולת תמיד הואי."