You're bringing up a few issues. Let's look at them separately and you'll find it's not as hard as it may seem to you now (though not easy either)
Different kanji spellings
Many common English words have got muliple meanings. Dictionaries usually list them as one entry. Reasons why this is not particularly troubling for English speakers include
- Meanings are often related, such as when a new meaning is derived from an older meaning (eg toilet: The word originally denoted a cloth used as a wrapper for clothes; then (in the 17th cent.) a cloth cover for a dressing table, the articles used in dressing, and the process of dressing, later also of washing oneself. In the 19th cent. the word came to denote a dressing room, and, in the US, one with washing facilities; hence, a lavatory (early 20th cent.) [OALD7])
- Some meanings are so close a normal speaker might not even think of it as two different meanings (inspection: ① an official visit to a school to check that rules are being obeyed, ② the act of looking closely at sth., to check that everything is as it should be)
- Some meanings are archaic (eg. breech: garment covering the loins and thighs) or less commonly used. Some meanings are not used standalone anD are part of fixed idioms.
- Which of two meanings is intended is usually obvious from the context if the meanings are drastically different
What does this have to do with Japanese? Well, there are some Japanese words - especially verbs - that are listed as one dictionary entries. The various meanings can be written with different kanji, but they should be thought of as the same word and similarly to English, aren't much of a problem.
For example, the 新明解国語辞典 has an entry for 変える that mentions 換える as variant spelling for some particular meanings.
The point here is that this is only a feature of the written langage and without kanji, you might not even have noticed.
Another example is あう (meet), which can be written as 会う・遭う・遇う・逢う and possibly a few more. And while 合う usually gets a separate entry, it shares a common origin with 会う. Makes me wonder how dictionaries would look like it kanji had not been introduced. A last example is 笑う (laugh) which is occasionally written as 嗤う to indicate a kind of deriding or mocking laughter.
Many Japanese words for an English word
When you say type in any English word into an English-to-Japanese dictionary, which dictionary do you mean? When I look for inspection, I find
- 2 words (検閲・視察) in the ふりがな英和辞典
- 2 words (検査・点検) in the コンピュータ用語辞典, with some examples such as acceptance inspection(受入れ検査).
- 27 words in an English-German dictionary (leo.org).
So even in two languages as close as German and English, we can find many possible words in the target language for a word in the source language (English). Keep in mind that this is a general problem when translating between two languages and only marginally related to synonyms and the difficulty of Japanese. Just because there are many different possible words in Japanese or German for inspection does not mean that these words are synonyms in Japanese/German - just that you could use these words in the right context.
The 研究社 新和英中辞典 lists 精査, 点検 and 検査 for the first meaning of inspection (looking closely at sth.) and then gives the following "example":
on first inspection
The example does not include the given possibilities! Why? Because the English is a set phrase and you should not translate word for word - producing a naturally sounding tranlation means rephrasing so that it resembles phrases and sentences native speakers would form.
You should rely less on English translations and think more about Japanese words an what they mean (preferrably in a monolingual dictionary) and look for example sentences that illustrate how a word is used.
Sometimes the explanation in a monolingual dictionary is enough to highlight the main idea or meaning of a word, and in extension, separate it from other words. For example, look up the words 視察 and 検査 in the 新明解国語辞典 and you'll find the former is concerned mainly with being present at the location of interest to "inspect" and being there to observe, while the latter is concerned more with the goal of the "inspection" - ascertaining whether there are faults:
視察: 自分で その場所に行って、実際の様子を見とどけること。「水害地の視察」
Also, note that many free English-Japanese dictionaries (such as jisho.org or tangorin.com) on the Internet use Edict/JMDict, which is essentially a project that collects all possible English words for a given Japanese word. Some "possibilities" are only possible in a very specific context and should not be included in a well-edited English-Japanese dictionary, so be careful when you use these. See this question about 響く for a good example.
As a final interesting observation, note that looking up, for example, the word outrage in an English dictionary of synonyms yields around ~25 "words with the same meaning" (Roget's 21st Century Thesaurus, Third Edition). What does this mean? Check it out and you'll find the words have some overlap, but are not completely synonymous. Should every Japanese-English dictionary entry that includes one of these 26 words also include the other 25?
It's true that when I search for words such as こうしょう, I get about ~30 different words (大辞泉). But keep in mind this includes archaic words not used anymore. And of the rest, some are more common, some are less common, and some may only be used in writing or technical texts. Also, in writing these words do not present much of a problem as the kanji make the meaning clear. In the spoken language people can use different words. Just because you can find many words for りょう etc. in a dictionary doesn't mean they are commonly used. That would almost be like somebody started learning English by reading books like Lord of the Rings or Game of Thrones - these folks would be wont to anguish and unlikely to display dissemblance regarding their minds on this matter.
For a real world usage, check out this example from a blogger who writes without kanji
いちぶの ゆうじんたちは よくしっていると おもうけれど、ここのところ、ぼくは かんじを いっさい つかわずに せいかつする という じっけんを してみている。
で、やってみたら、おもっていた よりも やれそうな きが してきて だいぶ じしんが ついたので、とうとう ここに せんげん することに します。
「ひらがなせいかつ」を すいしんする (もしくは うざいことするなあ、しねばいいのに、なんてことを いちいち おもわないと きがすまない ひとたちの きもちを さかなで することなど、そもそも いっさい いに かいさずに、ほろびゆく ちほう げんごである にほんごの、せんねんごを ほんきで うれう、もしくは うれう ふりをする) ぷろぐらむに さんか しませんか。
If you know a bit of Japanese, you should not have a problem deciphering this text, eg.
- 「ぼくは かんじを いっさい つかわずに」 → 僕は漢字を一切使わずに」
- ぼく could be 僕, 木, 卜, or 惚く, but only 僕 fits the grammar and context and is commonly used as a standalone word
- 「そもそも いっさい いに かいさずに」→「そもそも一切意に介さず」
- い has many kanji, but here it's obviously 意 because 意に介さない is a fixed expression.
- 「だいぶ じしんが ついたので」→「大分自信かついたので」
- じしん could 自信, 自身, 地震 or ~9 more less common words, but only 自信 makes sense combined with つく and the rest of the context
Tl;dr, learn more Japanese and get more familiar with the language and you will start feeling less overwhelmed.