Q Is a toilet plunger muktza? Can it be used on Shabbos? Can you use a wire snake? Can you unplug using a liquid like Drano?

A. Shulchan Aruch (O. H. 336: 9) rules that if a roof’s drain pipe is blocked with weeds and grass, causing a water leak and damage in one’s home, it is permitted to clear it privately with a shinui using one’s feet, since in case of loss, the Sages did not enact the prohibitions involved.
Mishnah Berurah (ibid. 47) explains that one can only clear partially the blockage so that it won’t interfere with the water flow. However, it is proscribed to totally remove the blockage, as this involves a prohibition of boneh or building, also tikun mono or fixing a utensil could be transgessed.
Shemiras Shabbos Kehilchoso (12: 17: n. 50) permits using a house plunger (non-professional) on a plugged sink when in great need.
In regards a toilet, many Poskim are lenient and permit using a plunger, since it involves the issue of kavod ha-brios (human dignity) and since the drain is wider it unplugs with more ease. (see Minchas Yitzchak 5: 75 and Chelkas Yaakov 3: 138).
Be’er Moshe (1: 29), Binyan Shabbos, p.. 18, 303, in the name of Horav S. Z. Auerbach zt’l also rule leniently.
Igrois Moshe (O.H. 4: 40: 9) rules that one may only unclog a sink with a plunger if it is a common occurrence and it is only partially plugged, and water can still flow slowly through.
However, Yabia Omer (5: 330), Yalkut Yosef (4: 2: 314: 25) and other Sephardic Poskim are stringent. So is Mishne halochos (6: 81, 82).
All Poskim agree that if another facility is accessible or if a Gentile is available, one should refrain from personally unplugging. Additionally, when possible it should be done with a shinui or change from the normal procedure, such as using the left hand.
Poskim are also stringent in the use of plumbing snakes and augers are they are seen as professional tools. (Orchois Shabbos (8: 31:) Horav Shlomo Miller Shlit’a maintains that if they have to be used, the obstruction is probably severe and unplugging it would be a prohibited melocho.
In regards to using chemicals to dissolve the drain blockage; 39 Melochos prohibits using them (4: 34: p.1027 ). Orchois Shabbos (8: 31: n. 38) assumes that it will depend on the opinions mentioned above. He mentions that the prohibition of molid or creating something new, may be involved. This being similar to the dissolving of fat stuck to dishes with hot water, that Mogen Avrohom (253: 41) prohibits.
Horav Shlomo Miller’s Shlit’a opinion in regards to a plunger is similar. In regards to using chemicals the Rov also maintains, that if the stoppage is not considerable, they could be used.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a