Because your LabVIEW program can't control when your hardware sends data, your first issue is going to be synchronisation with the incoming data and this will be determined by how the data is formatted. Is each item always terminated with a unique character (e.g. a carriage return) that never occurs elsewhere in the data? Then you can set the appropriate termination character in the properties of your VISA session and use a single VISA Read to return the data item as a string. On the other hand if it's a block of binary data terminated with a checksum or CRC, you may need to read one character at a time in a while loop and accumulate them in a shift register until you determine that you have a valid block of data.
Once you have your data you can decide what to do wit
h it. Does the data always come in a big block containing all the readings, or do the readings come individually in variable order, with some kind of identifier saying what each one is? In the first case you just need to split the block up into the appropriate chunks, in the second you might use a case structure to handle each type of data appropriately. Either way you'll probably find the Scan from String and/or String to Byte Array functions very useful.
If your LV program does anything else besides displaying/logging the data you receive, you'll probably want to use independent loops for the other processes. If you need to send data from the serial read loop to the rest of the program, consider using queues, notifiers or functional globals (aka LV2 style globals).
Looking at the examples in the LV installation and on this site will probably help, and you may get more help here if you can give us more detail about the format of the data.