How can I split a message in parts of similar size or smaller?
If the requirement is being able to reconstruct a message of $1280=160\cdot 8$ bits from $3$ parts that are among a set of $2^6$ type-able characters (say $10$ digits, $26$ uppercase letters, $26$ lowercase letters, and $2$ other characters, as in Base64), then no cryptography is required. Simply:


split the $1280$ bits of the message into $3$ nearly equaly-sized segments, here of $427$, $427$ and $426$ bits;
append to each segment something allowing to order the $3$ segments and making them a multiple of $6$ bits, e.g. here 00000,00001, 000010; now all messages are $432=72\cdot6$ bits, the two right bits identify the segment number;
encode each segment as $72$ type-able characters, each encoding $6$ bits.


Decoding, identifying and pasting together the segments is easy and left as an exercise to the reader.



If there is the additional requirement that knowledge of $2$ of the $3$ encoded segments should give no useful information about the message, then we need some cryptography. One simple method, optimized to reduce message expansion, is:


generate a random 128-bit $K$;
encipher the message with key $K$ (say using AES in CTR mode with implicit null IV);
split the enciphered message in $427$, $427$ and $426$ bits data segments as above;
XOR the first $128$ bits of each of the segments, and $K$, forming $K'$;
splits $K'$ into $3$ segments of $42$, $43$, and $43$ bits, append these to the respective data segments, and append the terminations 00000,0001, 00010, forming $3$ segment of $474=79\cdot6$ bits, that can be identified by their rightmost 2 bits;
encode each segment as $79$ characters each encoding $6$ bits.


Decoding is easy:


decode each segment of $79$ characters into $3$ segments of $474$ bits;
identify each segment by its right two bits;
remove the terminations, rebuilt $K'$, remove these;
XOR the first $128$ bits of each of the segments, and $K'$, forming $K$;
rebuilt the enciphered message;
decipher it using $K$.


If any of the encoded segments is missing, $K$ can't be formed again.

Notice that we must expand the message with random data somehow, or loose semantic security.