Oh wait, I get it, your first and second attempts in the question don't match one another. Codon 1 and codon 4 are the same?

EDIT: You really don't need to include the whole codon in your variable match, as only one or two bases vary. The following pattern works just fine.

import re

#p = re.compile('ga(:?u|c)au(:?u|c|a)gg(:?u|c|a|g)ga(:?u|c)')
#changed for readibility
p = re.compile('ga[uc]au[uca]gg[ucag]ga[uc]')
strings = strings = ['gauauaggagauaucguuagaggaaaagaucuauuuuaugguaauacacaugaaaguaa',
 'gaauauauaugaaggauugucgaacaaugguguaaaagcucgcuacgaaggugauacug',
 'gcgccacaguauggaaggcuaucacauguaaagcuaaggaagcugauaaauauuuuaga',
 'gcgaagauacugcggcacauaaucgaaauagguugggggaucgguauuuggauug',
 'gauauuggugau']

for string in strings:
    print(p.search(string))

Produces

<_sre.SRE_Match object at 0x24fde0>
None
None
None
<_sre.SRE_Match object at 0x24fde0>

As Giovanni says, checks for case and sequence validity would be a good addition, but are probably out of the scope of your question.

First you have to write some examples of sequences that should match your regex, and also some sequences that should not:

>>> good_ones = ('gauauugguggu', 
                  'gacauuggcggu', 
                  'gacauagggggu',
             )
>>> bad_ones = ('gaugauauugguggu',              # repeated codon
                  'auuggcgcu',                  # this case misses one codon
                  'gagauagggggu',               # wrong sequence
                  'acauuggcggu',                # this case misses one nucleotide
             )
>>> difficult_ones = ('GAUAUUgguggu',           # lower/upper case matters?
                  'gacattggcggt',               # T == U?
                  ' gacauagggggu ',             # leading spaces?
                  'ACGAGCgacauaggggguAGCTCGATCG',  # what if the sequence is within another sequence?
             )

Are these example correct? you should decide what you want to do in the latter examples: do you want to distinguish between lower and upper cases? between Us and Ts? what if the sequence has a leading or ending space?

Then, the regex you wrote is almost correct, but you can use a non-grouping operator (?: since you are not interested in making groups. Moreover, you should

>>> import re
>>> m = re.compile("^(?:gau|gac)(?:auu|auc|aua)(?:ggu|ggc|gga|ggg)(?:ggu|gac)$")
>>> for seq in good_ones: m.search(seq)
<_sre.SRE_Match object at 0x1666f38>
<_sre.SRE_Match object at 0x16665e0>
<_sre.SRE_Match object at 0x1666e68>

>>> for seq in bad_ones: m.search(seq)

>>> for seq in difficult_ones: m.search(seq)
???