You can use AES without an IV if you encrypt in ECB mode, but it's not a good idea. In ECB mode, the same plaintext always encrypts into the same ciphertext, so patterns in the plaintext can "show through" as recognizable patterns in the ciphertext. Use of ECB mode is discouraged.
To avoid the problems of ECB mode, the cipher can combine each block of the plaintext with the result of encrypting the preceding block, which is known as CBC mode. This prevents patterns in the plaintext from being recognizable in the ciphertext, since the same plaintext will produce different ciphertext depending on where it's located in the stream. But if you're combining each block with the one before it, what do you combine the first block with? That's what the IV is for.
Sending an IV together with the ciphertext isn't a big deal. It's small, just 16 bytes for AES — hardly "overkill" to transmit. Think of it as part of the encrypted file.
Your question brings up a related question of key management, though. AES is a symmetric cipher, which means that whoever decrypts the data needs to have the same key that the phone used to encrypt it. If you have lots of phones all sending AES-encrypted data to a server, that's lots of different keys that you have to keep track of.
(I'm assuming that each phone uses a different key, because otherwise you have no security. If all the phones encrypt using the same key, anyone who has your app can extract that key and use it to decrypt data from other people's phones.)
If you were using TLS to send data to the server, it would take care of generating a temporary encryption key for each connection, and automatically encrypting the data on the phone and decrypting it on the server. You wouldn't have to deal directly with AES at all.
But since you're implementing your crypto "manually", you also have to implement your key management manually. How does the server know the phone's key? The "right" answer would be to use Diffie-Hellman key exchange. The "wrong" answer would be for the phone to generate a key and then send it to the server, because anyone who could intercept an encrypted file could intercept the key too.
You should consider using public-key cryptography for encrypting the files sent to the server. That way, the phone only needs to know the server's public key, which doesn't need to be kept secret.