Ordinal string check
Python,  56  53 bytes
-3 thanks to  (use unique letter inclusion instead of penultimate character equality)

lambda v:'hsnrhhhhhh'[(v[-4:-3]!='1')*int(v[-3])]in v

An unnamed function.
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How?
Since all input (here v) is guaranteed to be of the form \d*[st|nd|rd|th] we can just test whether a character exists in v which we expect to be there if it were correct (s, n, r, or h, respectively) - that is &lt;getExpectedLetter&gt;in v.
The last digit usually determines this:
v[-3]: 0 1 2 3 4 5 6 7 8 9
v[-2]: h s n r h h h h h h

...except when the penultimate digit is a 1, when all should end with th and hence our expected character must be h; to evaluate this we can take a slice (to avoid an index error occurring for inputs with no -4th character) v[-4:-3]. Since 0 maps to h already we can achieve the desired effect using multiplication prior to indexing into 'hsnrhhhhhh'.