Words and Explanations 1

ἐν τῷ ἀγρῷ πονεῖ

he works in the (or: his) field.
We had: he lives in the country, i.e in the fields (plural): Where?
οἰκεῖ ἐν τοῖς ἀγροῖς
So now we have the singular: Where?
ὁ ἀγρός, ἐν τῷ ἀγρῷ
ὁ κλῆροςἐν τῷ κλήρῳ
ὁ οἶκος, ἐν τῷ οἶκῳ
Just another form (which happens to be called "dative" form) to clarify the meaning: where? position
 

τὸν γὰρ ἀγρὸν σκάπτει

again: γάρ = for (because), always takes 2nd place
for he is digging his field:
see him dig away furiously (he's ἄοκνος καὶ ἰσχυρός, remember?)
Who σκάπτει your garden? How does he (or she) σκάπτει ? See them do it!
 

τοὺς γὰρ λίθους ἐκ τοῦ ἀγροῦ φέρει

ὁ λίθος the stone
lithography is writing on stone, paleolithic was the oldest of the stone ages, then came mesolithic (middle) and neolithic (new, not because the stones were new, but because people knew better how to fashion them)
τοὺς λίθους φέρει is the plural form of:
τὸν λίθον φέρει
see picture 1a:
φέρει δὲ τὸν μόσχον
so if he were to carry several calves (since he's so ἰσχυρός that shouldn't be a problem), we'd say seeing him:
φέρει τοὺς μόσχους
Similarly: σκάπτει τοὺς ἀγρούς
τοὺς πόνους φέρει
τοὺς οἴκους βλέπει he sees the houses
When coming across these forms, just visualize the action and tell yourself: this is how we say.... when we mean ... (I accuse, see, carry him and not he, so -oν
or, in the plural, I accuse, like, carry them, not they, so - ους

And after position (where is? dative) we get to origin (out of where? from where?). So we'll need yet another case-form:
ἐκ τοῦ ἀγροῦ out of the field.
In the same way : ἐκ τοῦ οἴκου
In the same way : ἐκ τοῦ κλήρου
Again, visualize and tell yourself, this sounds right for getting out of a place. You won't remember it immediately, but eventually it will became automatic. Learning the rule: after ἐκ we have to use the genitive is not going to help you half as much as your ears and your imagination will.
So, each time you come across a new form, just visualize the action and tell yourself: this is how we say when we:
ἐν τῷ ἀγρῷ see somebody in the field doing something or other, like:
ἐν τῷ ἀγρῷ σκάπτει he's digging somewhere in his field, digging a grave maybe, or a hiding-place for his treasure
τὸν ἀγρὸν σκάπτει see somebody digging the field, the whole of it
τοὺς λίθους φέρει ἐκ τοῦ ἀγροῦ see him carrying all those heavy stones out of his field, out of his way, out of his life (ἐκ τοῦ βίου)

Of course you won't remember all of them at once, nobody expects you to. But through repeatedly meeting these strange forms (strange to us, not to the Greeks) and imagining the contexts, the scenes, concentrating on their meaning rather than their grammatical definition and function, you'll end up becoming familiar with them, automatically, for the wrong form sounds wrong because it is meaningless. A small child doesn't know anything about cases and declensions and yet gets it all right, after a time. What we could do as little children, we still can, the ability is still there, but all our abstract, theoretical learning has made us forget our innate capabilities. Give a bright 5 year old the opportunity to learn a language using lists of words and rules of grammar and he'll end up knowing very little, unless you give him quite a few years' drilling. Now take a dim 5 year old and put him in a environment where he has to use the language to interact with others and he'll learn pretty fast. Ever thought why? Listening to what sounds right and what sounds dumb does the trick. He doesn't want to be taken for a dummy by his peers. Not if he can help it. Unless he's really mentally handicapped.