Mobile Sheets - available at the Google Play Store - There is no question, this is the sheet music app for Android. With this app on a tablet, you can entirely replace your choir binder. It extremely full-featured and is in active development with new features are added all the time.
Perfect Piano - There are lots of free piano apps for plunking notes, but this app gives you access to all 88 keys by scrolling to whichever part of the keyboard you like. Not only can you control the octave you're in, but you can choose exactly where the active part of the keyboard starts. (It doesn't have to be a C or an F, for example.) So, I think it gives the most flexibility for choosing exactly which keys are available at any one time and you can easily move the slider to suit the range of each song.
Dropbox - Dropbox isn't my general cloud provider of choice, but my sheet music app has built-in support for importing music directly from Dropbox, so it's what I use for choir pdf and audio files.
ForScore - This is the sheet music app for Apple iOS devices. It is extremely powerful, and like Mobile Sheets for Android, can completely replace your choir binder. ForScore even includes an in-app piano keyboard that can pop up while you are reviewing your music, so you won't need a separate piano app.
Dropbox - Like Mobile Sheets, ForScore has built-in support for importing music directly from Dropbox, so it's the best choice for your choir pdf and audio files.
Resources around the Web
Cyberbass and Choralia both provide part-by-part learning tracks free for listening online for many major choral works. It's always a good idea to check these sites when you start a piece to see if there are resources here!
ChoralWiki and the International Music Score Library Project both contain thousands of public domain pdfs of music scores. Although you can scan a copy of your physical score to add to your device, an electronic copy will be much easier to use (and often easier to read).
YouTube is a great resource for finding recordings of other choirs performing your songs as well as for finding part-by-part learning tracks that various organizations, music teachers and students have uploaded themselves to their own accounts. NOTE: When searching for songs on YouTube it is very important to include the name of the arranger in your search. You want to make sure you're finding performances of the exact same arrangement of the song you are learning. You may also need to include the voicing (e.g. SATB or TTBB) or look at the video to make sure you see both men and women performing if you want a mixed-voice rendition. For part-by-part tracks, include the name of your voice part (e.g. "alto" or "tenor") in your search, as well. Be sure to check out the Choir Parts YouTube channel for many classical part-by-part learning tracks! Vimeo and SoundCloud are two other sources you may wish to search.
Many times if you search Google for the title and arranger of a song, you can find a listing for it on a publisher's website or online sheet music store for sale. JW Pepper and Hal Leonard are two excellent resources for many popular arrangements. Often, these listings will have professional recordings of the songs that you can listen to online. Sometimes they are only 30 second clips, but very often you can hear the entire song performed by studio musicians. These can also be very helpful for learning your part because the recordings and individual voices are quite clear. Cypress Choral is an excellent Canadian Choral publisher with many recordings of their arrangements available online.