I've heard quite a few times that in WW2, the US never officially declared war on Germany. Was this a technical oversight, or was there a strategic reason for intentionally not doing this?

I'm not sure who exactly would have said/written this, because the United States most certainly did officially declare war on Germany.

The United States has formally declared war 11 times (Britain in 1812, Mexico in 1846, Spain in 1898, Germany and Austria-Hungary in 1917, Japan, Germany and Italy in 1941, and Bulgaria, Hungary and Romania in 1942). Germany actually holds the unique distinction of being the only country that had formal declarations of war passed by the United States against it twice.

The US declaration of war on Germany on December 11, 1941 was in some ways a formality, as Germany itself had formally declared war on the US earlier that day. u/Kieslowskifan has more information on German planners' thinking behind their declaration of war here. The fact that Germany had already declared war on the US no doubt caused the higher votes for the US declaration than had been the case against Japan three days earlier: the Senate voted 88-0 for the resolution, compared to 82-0 against Japan. The House voted 393-0, compared to 388-1 for the declaration of war against Japan. That single vote against war with Japan was Republican Jeannette Rankin of Montana, who had voted against war with Germany in 1917. For the declarations of war against Germany and Japan on December 11, 1941 she declared herself "Present", and effectively abstained (but did not vote against) those declarations.

Interestingly, the December 8 declaration of war against Japan was the template for the December declaration of war against Germany - literally. The Japan resolution was a literal draft for the Germany declaration, with "Japan" crossed out and replaced with "Germany".

Now, it is true that Germany and the United States were shooting at each other and taking casualties before December 11, and this might be where the confusion comes from. The United States had declared a Pan-American Security Zone in October 1939. In theory this was a zone for maintaining neutrality of North and South American countries during the war - it was formally requested by Panama. The United States patrolled this zone with air and naval forces and reported the movement of belligerents' warships in the area - this effectively became a benefit to the Allies in open-channel reports of German submarines, which benefitted convoys sailing from Canada to Britain. This was the start of eventually much deeper material cooperation between the United States and British Empire: the Destroyers for Bases agreement was signed on August 30, 1940, and Lend-Lease was passed on March 11, 1941. President Roosevelt formally extended the Security Zone to just shy of Iceland in April 1941, and in late June 1941 the British military turned over its occupation of Iceland to US forces. US neutrality was increasingly a formality that covered substantial material support and cooperation with British forces (in broad terms this is similar to US support for a country in a current conflict that I will not discuss because of the 20 year rule). The Lend-Lease Act contained a rider stating that "Nothing in this Act shall be construed to authorize or permit the authorization of convoying vessels by naval vessels of the United States".

Part of the question would be why the US went to these lengths to preserve formal neutrality. In part it was because of US domestic politics - in the late 1930s there was a substantial bloc of the US electorate (and of members of Congress) who wanted no part in an obviously-brewing European war. This electorate and its politicians tended to be Progressive Republicans from the US West and Plains states - Representative Rankin being one, and Senator Gerald Nye of North Dakota being a prominent such member in the Senate. Nye lead a commission (named after himself) in the 1930s, which investigated the causes of America's entry into World War I, and largely blamed the US financial and arms industry, and was instrumental in the passing of Neutrality Acts in 1935, 1936 and 1937, which taken together essentially forbade any US material support (government or private) in basically any armed conflict zone anywhere. The German invasion of Poland in 1939 saw Roosevelt lobby Congress to repeal those Acts, and he was successful in a measure, replacing them with a new Neutrality Act that allowed private individuals more latitude in their action, and legalized material support for belligerent powers (meaning effectively Britain and France - unlike in World War I the US wasn't even attempting to sell anything to Germany) on a "cash and carry" basis - those powers had to pay in hard currency and take supplies away in their own ships. Roosevelt himself, at a press conference after the passage of Lend-Lease, denied that the US was even considering armed escorts of convoys ("shooting comes awfully close to war, doesn't it?"). However, Secretary of War Henry Stimson and Secretary of the Navy Frank Knox (both prominent Republicans, by the way) had gone on record as advocating for naval escorts, and also stating that the President had Constitutional Authority to authorize this - a debate between the war powers of the Presidency and Congress that has continued to this day.

Anyway, the armed escorts were a very divisive issue among the American public (bare majorities supported naval escorts even at the risk of war, but bigger majorities wanted to stay out of the war, and 70% of respondents thought the US had done enough or too much to help Britain) that in turn caused Roosevelt to move in contradictory ways - publicly denying even thinking about armed escorts, while internally the administration asked the Navy to examine the question, and in April 1941 calling for "Hemisphere Defense Plan Number 1", involving moving more naval assets to the Atlantic and adopting armed escorts, before rescinding the order barely a week later (extending the Pan American Security Zone eastwards was a compromise).

The extension of the Security Zone meant that now US forces were in an area that overlapped with Germany's declared zone of combat in the Atlantic, and sooner or later incidents occurred. The destroyer USS Niblack, after picking up survivors of torpedoed merchantmen, dropped depth charges on what it thought was a U-boat (subsequent investigations revealed nothing was actually there). The American merchant ship Robin Moor was then sunk in the south Atlantic with no loss of life in May 1941 - this was controversial over the lack of aid supplied to the crew in lifeboats and the sinking happening outside of the declared zone of combat, but Roosevelt demurred in instituting armed escorts. The meeting between Churchill and Roosevelt at Argentia, Newfoundland in August 1941 was most famous for the Atlantic Charter, but Churchill pressed Roosevelt for armed escorts, if not an outright declaration of war against Germany. Roosevelt agreed to the escorts, but still agonized as to how to break this to the American public.

The incident that finally provided the pretext involved the destroyer USS Greer off of Iceland on September 4. The Greer, following the letter if not the spirit of the Security Zone, was aggressively following German submarine U-652 and reporting its movements. A British plane dropped depth charges, causing the U-Boat captain to fire torpedoes at Greer, who then dropped depth charges on the U-boat. No ship sustained any casualties and all departed from the scene. Roosevelt used this incident for a radio address on September 11 declaring that Greer had been the victim of an aggressive attack, and that U-Boats were "the rattlesnakes of the Atlantic" that required a "shoot on sight" policy: "American naval vessels and American planes will no longer wait until Axis submarines, lurking under the water, or Axis raiders on the surface of the sea, strike their deadly blow ... From now on, if German or Italian vessels of war enter our waters [ie, the Security Zone] ... they do so at their own peril." Six days later the Canadian navy handed over the first fifty ship convoy to five US destroyers for armed escort, and the US and Germany were on course for an undeclared shooting war in the Atlantic. Notable incidents hereafter were an engagement of USS Kearny with U-568 on October 17, resulting in Kearny being struck by a torpedo and suffering 11 KIA, 22 wounded, and the engagement of U-552 with USS Reuben James on October 31, which saw the American ship sunk and 100 KIA (only 44 survived). The shooting war itself would be cited as pretext in the German declaration of war of December 11.