I'd more or less agree with the above answer, apart from the part about the difference between English and American pronunciations.

Dictionary.com has the two pronounced as /ˈwɔrˌʃɪp/ [wawr-ship] for warship, and /ˈwɜrʃɪp/ [wur-ship] for worship. These are about how I'd expect them to sound as a British English speaker.

Merriam-Webster suggests 'wər-shəp or 'wòr-shəp for worship. I'm not quite sure about either of those.

Warship : wôrˌSHip ( more like Wor-Ship )

Worship: wərSHəp ( more like Wer-Ship )

The 'a' in Warship is like the 'a' in Law. It is a sound that is hard for a non English speaker to pronounce, try making 'law' and 'low' sound different, they should sound very different and this is part of the same issue.

The 'or' in Worship is like 'err' in "to err on the side of caution", or the mechanical sound that is associated with spinning, 'whirr', as in "The machine whirred past".

I cannot hear a difference between the two at all. If I heard someone say either word out of context, I would have no idea which one they meant. (And for what it's worth, detecting audible differences comprises much of my life).

On the other hand, I agree with @Kelly C Hess -- despite their similarity, I am pretty sure I have never confused them. Fortunately there are probably very few cases when it would be ambiguous in context.

I'm pretty sure, when I was a kid in Toronto, that we pronounced the word worship like "warship", as in, a ship of war. I'm not sure I have any way to prove that.

Sounds like....

The first syllable of worship is pronounced the same way that the word were is pronounced. In contrast, the first syllable of warship is pronounced the same way that the word wore is pronounced. Those two sound-alike words — were, wore — are unlikely to be pronounced the same as each other in most accents, or maybe in any.

The second syllable of worship is pronounced the same way the second syllable of the word bishop is pronounced. In other words, it’s a very short, unstressed syllable with a fully reduced neutral vowel, the one we call schwa. In contrast, the second syllable of warship is pronounced almost as though it were the full word ship. It’s a separate morpheme in a compound word that retains its original character, and it is not reduced.

Looks like....

Precisely how you represent these two words phonetically very much depends on which particular accent we’re talking about. The respective variants can sound quite different from how each other sounds, and their corresponding phonetic representations can often look even more unalike than the sounds.

All that variation aside, one reasonably simple representation that works for rhotic speakers with monophthong vowels before rhotics would be to use /ˈwəɹʃəp/ for worship and to use /ˈwoɹˌʃɪp/ for warship. Notice how the second of those has a bit of secondary stress in its second syllable that the first one lacks.

You should also be aware that most North American speakers, especially rhotic ones, neutralize the lax–tense (or open–close) phonemic distinction (/ɔ‑o/, /ɛ‑e/) before rhotics, perceiving each to always be the close variant in that position. That makes wore have the same tense /o/ vowel as woe has for them, not the lax /ɔ/ vowel they have in the word wall.