Not Gilbert Goodmate. This particular game is from the 1990s.

Spoken by the same character:
"I'm reminded of a red tide on the Jersey shore after a laxative convention!" :r

The second quote evades me but the first one kind of sounds like Full Throttles style dialogue.

This second quote makes think of Duckman.

Not Full Throttle or Duckman either. (Shany's getting warmer though, the speaker is not a human character. ;))

Here's an exchange by the game's title character and his friend (who spoke the previous two quotes):

"I suspect a very large set of nuts can be loosened with this."
"Do you mind?! That is not the kind of thing a dog likes to hear! How would you like to donate your manhood to veterinary medicine? It's absolutely savage!"

sam&max?
a wild guess but.....

Flux in Toonstruck? I'm not sure Flux is actually a dog, but it sounds like the kind of thing he might say.

Nope, not Sam & Max or Toonstruck either (the game is a comedy).

One more quote by the title character (not a dog):
"This is more enigmatic than a Sanskrit fortune cookie!"
(The other character, his travelling companion, who said the first two quotes, is indeed a dog.)

I never actually played the game but am thinking Wallace & Gromit's grand adventures maybe? Or any of the other Wallace and Gromit adventure games?

Kuala Lumpur Journey to the Edge?

Hurray, Shany finally got it! :D (These lines were spoken by Koala Lumpur and his companion, Dr. Dingo Tu-Far.)

I keep forgetting about that game, it rarely gets mentioned


Okay, here's one:

- Character 1: "Hey... that wasn't half bad!"
- Character 2: "No, [character 1], it was all bad!"

I'm probably way of the mark here but it reminds me off Runaway 2. Something the soldiers in the temple could've said

No, sorry, it's from an older game.

Sounds like something from Leisure Suit Larry... Possibly #3?

You're getting very close.

Okay... Larry 7? (Anette Boning might say something like that... But so could all the women Larry have slept with...)

Yes, Larry 7. It's an exchange between Larry and the Narrator after Larry tastes something in the kitchen.

The kitchen had the funniest lines in the game...

Scratch and sniff kitchen scene?

I agree that the kitchen was full of great lines, for those who were willing to look everywhere.

OK, new line:

Oh Cod, it makes me Eel when people Carp and Whale just for the Halibut, with no Porpoise. I'm Net that kind of Buoy, Sea? I'm Shore tired of Gills in School with their Tails of Roe.

This should be very easy... I'm tempted to ask for more than just the game's name --- but then again I was not able to do it with the previous quote, so I won't.

Now I feel stupid if it's so easy. I'll probably kick myself when I see the answer but I'll guess Eco Quest.