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I managed to make a table but the caption (or any text I add after it) is in the middle of the table, as if the table ended after the second row. I couldn't find a similar question so I decided to ask myself.

Without the caption, or any text before/after it, the table looks almost how I would want it to look.

documentclassreport
usepackagemultirow


begindocument

This is some text and here is a reference to Table reftable:mytable. 


begintable [h] 
 centering
 begintabular c c c \
 textbfColumn A & textbfColumn B & textbfColumn C \ 

 hline

 multirow3*textbfTest1 
 & multirow3*shortstack[l]line1 \ line2 \ line3
 & multirow3*shortstack[l]line1 \ line2 \ line3 \ 

 multirow6*textbfTest2 
 & multicolumn2c multirow6*shortstack[l]line1 \ line2 \ line3 \

 multirow9*textbfTest3
 & multirow9*shortstack[l]line1 \ line2 \ line3
 & multirow9*shortstack[l]line1 \ line2 \ line3 \ 

 multirow12*textbfTest4 
 & multirow12*shortstack[l]line1 \ line2 \ line3
 & multirow12*shortstack[l]line1 \ line2 \ line3 \ 

 endtabular
 labeltable:mytable
 captionThis is the caption. 

 endtable

enddocument

As a side note, the referencing also isn't working properly for some reason?. I wanted the sentence to say

[...] here is a reference to Table 1.

and instead it just says

[...] here is a reference to Table .

I've managed to use ref with other tables but not this one.

multirow<nrows><width><text> spreads text (vertically) across <nrows> rows of width <width>. If <width> is given as *, it uses the natural width of <text>. So, for example, using multirow12*<...> means you want to spread that specific cell over 12 rows. It's obviously incorrect since each TestX you want to spread over only 3 rows.

Here's a slightly different implementation (since you don't need multirow here) using makecell:

documentclassreport

usepackagemakecell

begindocument

This is some text and here is a reference to Table~reftable:mytable. 

begintable [h] 
 centering
 begintabular c c c
 textbfColumn A & textbfColumn B & textbfColumn C \ 
 hline
 textbfTest1 
 & makecellline1 \ line2 \ line3
 & makecellline1 \ line2 \ line3 \ 
 textbfTest2 
 & multicolumn2cmakecellline1 \ line2 \ line3 \
 textbfTest3
 & makecellline1 \ line2 \ line3
 & makecellline1 \ line2 \ line3 \ 
 textbfTest4 
 & makecellline1 \ line2 \ line3
 & makecellline1 \ line2 \ line3
 endtabular
 captionThis is the caption. 
 labeltable:mytable
endtable

enddocument

Note how the label comes after caption in order to achieve the correct reference. See Why does an environment's label have to appear after the caption?.

As I write in the comment to the question, you have misunderstood how multirow calculate spanning of rows, but it is easily fixed. Just add 3 all places (i.e instead of 6, 9 and 12).

To fix the misplaced caption, and if you want to use your original code, you have to add extra space after the multirow row to create enough space for the spanned rows. Since you span three rows, you may either add two rows (&&\) or extra height at the end-of-row command (\[<height>]. I added two normalbaselineskips so you have space equal three rows.

The safest place for the label is inside the caption command. Then it will not fail.

documentclassreport
usepackagemultirow


begindocument

This is some text and here is a reference to Table reftable:mytable. As you see, the table is a float, and since you have available space, it is place at top of the page. Do not mess around with placing floats before you have finished all creative writing. Everting you do, will be invalid when you add more text. 


begintable
 centering
 begintabular c c c \
 textbfColumn A & textbfColumn B & textbfColumn C \ 
 hline
multirow3*textbfTest1 
 & multirow3*shortstack[l]line1 \ line2 \ line3
 & multirow3*shortstack[l]line1 \ line2 \ line3 \[2normalbaselineskip] % Add more space
multirow3*textbfTest2 
 & multicolumn2c multirow3*shortstack[l]line1 \ line2 \ line3 \[2normalbaselineskip] multirow3*textbfTest3
 & multirow3*shortstack[l]line1 \ line2 \ line3
 & multirow3*shortstack[l]line1 \ line2 \ line3 \[2normalbaselineskip]
multirow3*textbfTest4 
 & multirow3*shortstack[l]line1 \ line2 \ line3
 & multirow3*shortstack[l]line1 \ line2 \ line3 \[2normalbaselineskip]
endtabular
captionThis is the caption.labeltable:mytable 
 endtable

enddocument

A variant code, also based on makecell, combined with multirow – and booktabs, to add some padding around rules. I added some vertical spacing to separate the groups of three lines. Also, a reference to requires a label command (after the caption) to work.

documentclassreport
usepackagemultirow
usepackagemakecell, booktabs
renewcommandtheadfontnormalsizebfseries


begindocument

This is some text and here is a reference to Table reftable:mytable.

begintable [h]
 centering
 begintabular c c c \
 textbfColumn A & textbfColumn B & textbfColumn C \
 midrule
 multirowthead3Test1 & line1 & line1 \
 & line2 & line2 \
 & line3 & line 3\
addlinespace
 textbfTest2 & multicolumn2cmakecellline1 \ line2 \ line3 \
addlinespace
 multirowthead3Test 3 & line1 & line1 \
 & line2 & line2 \
 & line3 & line 3\
addlinespace
 multirowthead3Test 4 & line1 & line1 \
 & line2 & line2 \
 & line3 & line 3\
bottomrule
 endtabular
 labeltable:mytable
 captionThis is the caption.labeltable:mytable

 endtable

enddocument