Can you give us a little more to go on? Then maybe someone here can help. When? Where? Birth dates? Are they siblings? Were they living in USA... where/when? Birth, death? Have you searched census records?
Did they stay in the places shown above? You should certainly see what you can find in the 1910 US Census. The easiest way to do that would be with a search on Ancestry.com. Have you done this before? If you are not a member, perhaps someone on this site is and can do a look up.
For Paul, is that Grant County? Grant County has a historical society. They helped me with a little information about my grandfather who lived near there briefly (about 1911).
Do you have birthdays?
Do you know where they went later on?
Do you have death dates and places? Death certificates often contain useful information. Obits?
To go back in time, probably the most valuable piece of information would be the parish in Sweden where he came from. Most records in Sweden were kept by parish.
Ancestry.com may also find passenger list for a ship from Antwerp arriving NY 8 Apr 1902. It would they show if the all traveled together. Antwerp is an unusual place for a Swede to emigrate from. Do you know why? A typical path would be from Goteborg to Hull to Liverpool to NY.
Looking at Ellis Island Emil Wahlen was of Swiss nationality. If so, he probably wont be found in the swedish census.
Paulson on the other hand is a swedish surename. We sure could use some more information. In swedish census of the year 1900 I find 117 persons namned Joel. No one got a surename starting with the letter V or W that sounds like Wahlen.
888 persons named Emil but no one namned Wahlen. There´s three men named Wallin but none of them has a son mamned Joel.
Frustrating. Wahlen certainly sounds Swedish. Leaving from Belgium would lend credibility to Swiss. There must be a story to explain all of this. I could go either way with "Emil."
Lots of people confuse Sweden and Switzerland (although you would expect more from Ellis Is). I get that all the time. Well Im off to my Scandinavian symposium for all day Saturday. Raining hard in L.A.