lǎohǔ=tiger (虎), which literally means "old tiger (老虎)".
xiāngjiāo=banana (蕉), which literally means "fragrant banana (香蕉)".
dàsuàn=garlic (蒜), which literally means "big garlic (大蒜)".
I consider 老虎, 香蕉 and 大蒜 should be categorized as the "descriptive noun", that is a name (noun) assigned to serve a purpose.
老虎 = 虎 Both are noun means "tiger". In it, "老" is not describing the age of the tiger, thus it shouldn't be considered an adjective. For example, a puppy/young tiger is called "小老虎" (in here 小 is an adjective), and an aged tiger is described as "上了年紀的老虎" (in here "上了年紀的" is the adjective).
I am not aware of the exact reason the name was given, but I think "老虎" was referred to the mutually grown tiger that was considered as "猛獸", which was an animal to be afraid of. Thus, it started by the elders using the phrase "老虎來了" to scare the little kids into behaving. Similar to the use of the term "巫婆 (an old female witch)" rather than "巫女 (a female witch)", "老虎" is a much scarier name than "虎", which sometimes depicted as a beautiful, cute animal on paintings and, on decorations such as on child dresses (虎頭鞋, 虎頭帽), symbolized health and strength.
"香蕉" is a type of "蕉" that has many varieties, such as "芭蕉" or "美人蕉". It is correct that it was named due to its fragrant smell. In here, "香" seems an adjective, but I would say it is the necessary addition to distinguish "香蕉" from other varieties of the same biological family (type). So, I consider "香蕉" as a noun.
I don't consider "大" in "大蒜" is an adjective, as it is not concerning the size (big), but, similar to "香蕉", was added to "蒜" to distinguish itself from the varieties of the garlic family, such as "蒜頭", "蒜苗"...etc. So I would consider "大蒜" as a noun.
There are English examples of the descriptive nouns, such as "green bean", "roast coffee" and "Franch fry"...
Edit On "how to say,
an old tiger: 一頭(隻)"上了年紀的"老虎.
a fragrant banana 一根(隻)"很香的"香蕉.
a big garlic 一顆(粒)"相當大的"大蒜.
Note, words in quotes are adjectives.