How do you learn words that don't have translations into your language? Obviously start by reading the definition in PIV and other dictionaries to understand what it means. If I read the definition and can't put an English word to it, it doesn't really enter my vocabulary. I have passive knowledge of it. I'll get it if someone else uses it or I read it but I just don't end up using it. Recently on my flash cards I started putting what the word means and not just the translation and I think that helps, what else can you do?
In my AnkiDroid I usually try to put pictures if possible because I find them easier to remember. You can just search for a suitable image on Google and copy it in. If the word is abstract, sometimes it can be useful to draw a diagram.
Another good tactic is to put the word in a few example sentences. It’s usually easier to remember a phrase than just a dry definition. If you are using AnkiDroid you can make a “Cloze” card where you blank out part of the example phrase and then on the “back” of the card it will be revealed.
Personally I tend to avoid using translations in flash cards even if the word does have a clear translation to English, because I think it helps to immerse yourself a little more and to get out of the mindset of constantly translating when you speak.
I question some of the premises in the question. Words don't "have translations" in other languages. Words express meaning, and people render these meanings into different languages. If we grant (as I do) that all languages are fully expressive, then it should be possible to express ideas equally into all languages. Therefore, in trivial sense, all words do "have translations" in other language.
There are lots of words that I know in Esperanto that actually do "have" straightforward translations (at least according to bilingual dictionaries), and yet I sometimes have trouble translating them simple because I did not learn this word by reading a translation. (In some cases, it's possible I did, but that it's been years since I've thought about this.)
A recent example of this is from my video "Kampara Mensogo" in which I used the word konsterniĝi. I used it correctly. I knew what it meant. It made sense in the context. But when making the English subtitles, I found myself stuck on what word to use.
There will (or there should) come a time in your Esperanto learning where you learn new words the same way you learn new words in your native language - by seeing them in different contexts, asking people to explain them to you, and by looking in a monolingual dictionary -- but mostly by seeing them in different contexts. Advancing in a language is not a process of becoming a better translator, but of being exposed to as much good Esperanto as possible and immersing yourself that way.
The more good Esperanto you put in, the more good Esperanto will come out.
Learning isolated words is almost never the best way to learn them. Memorise phrases, or even whole sentences, and, eventuale, write them on your flashcards, with or without pictures. Even in the simplest cases, when a perfect translation exists, it is easier and functionally more useful to remember la libro estas sur la tablo than the pairs libro ⟷ book, tablo ⟷ table and the very dubious pair sur ⟷ on.
There is an ongoing debate in the relevant forums about how effective “cloze” cards really are, but nobody doubts the effectiveness of learning words in their proper context.