Only If Sources Beyond the Player's Handbook Are Used
Omitted from the online sorcerer description is the following from the Player's Handbook:
[The sorcerer's] new spells can be common spells chosen from the sorcerer/wizard spell list (page 192), or they can be unusual spells that the sorcerer has gained some understanding of by study. For example, a sorcerer with a scroll or spellbook detailing an unusual sorcerer/wizard spell (one not on the sorcerer/wizard spell list in this book) could select that spell as one of his new spells for attaining a new level, provided that it is of the right spell level. (54)
Emphasis mine. Using a very hard reading of the rules as written, if the DM determines the sorcerer can gain "some understanding of [the spell cure light wounds [conj] (PH 215-6)] by study" from the scroll and the spell cure light wounds appears on the Sor/Wiz spell list in another source other than the PH, the sorcerer can add it to his spells known.
As the above is largely campaign-dependent, it needn't be a scroll. The DM determines what exactly the sorcerer can study to gain this understanding (e.g. ancient dragon scales possessing the secrets of weird magic, the corpses of magical minions, the drippings of sacred candles).
I am, however, unfamiliar with a published setting or source that adds cure spells specifically and directly to the Sor/Wiz spell list.
However, another source can totally be the DM's campaign notes. Thus, in a campaign that amends the Sor/Wiz spell list, the sorcerer could, upon understanding the spell via study, select that spell as a new spell when he reaches the next level if the spell's on the Sor/Wiz list at the appropriate level.
The DM should look askance at a player who claims his authorship of another source on a cocktail napkin amends his character's spell list, unless the source is accompanied by an appropriate bribe.
There are other arcane spellcasting classes that use spellbooks, like the magus. The alchemist has a “formula book” that works mostly the same way, and the witch has a familiar that functions like a spellbook for her.
In all of these cases, however, learning from scrolls is reserved for a class with very wizard-like spellcasting, that is, they must prepare exactly which and how many of each spell they know in advance.
As you note, the divine spellcasters who, like the wizard, prepare spells ahead of time don’t need to bother with spellbooks at all. Clerics, druids, and similar divine spellcasters can pray for any spell on their list, even one they have never seen before. In effect, you can think of the gods they pray to as being giant spellbooks that already have every spell available ready to go.
On the other side of the coin, we have spellcasters that do not have to prepare their spells ahead of time. The sorcerer is the quintessential example, but others exist, including some like the oracle that are divine (as you note). These “spontaneous” classes do not keep a spellbook or similar, and they cannot take advantage of the rules for copying a scroll into a spellbook. Scrolls, for them, can only be used as a scroll, not used to learn a spell. To learn a spell, they need the vastly more expensive page of spell knowledge, or the even more expensive ring of spell knowledge (which then does allow them limited ability to learn spells from scrolls and other sources).
The advantage to spontaneous spellcasters is that they are free to use these spells in any combination they like, up to their spells per day limit, where spellcasters that prepare have to choose exactly how many of each spell they want. However, generally speaking, the advantage of having access to so many spells is vastly superior, so clerics and druids and wizards are generally better than oracles and sorcerers and the like.
Best Answer
No, a wizard cannot cast a bard spell, even if it is on an arcane scroll that he copies into his spellbook. The first sentence of the Wizard class ability entry for "Spells" is:
If the spell isn't on the list or a unique spell you've researched and gained DM permission for, you can't use wizard spell slots to cast it.
By the RAW I can't find anything that would prevent you from learning or scribing a non-wizard spell into your spell book if it's on an arcane scroll, but it would be a waste of gold and time without being able to cast it.
Furthermore, the Eberron Campaign Setting Errata File includes the following:
As the scrolls he makes using the artificer's Item Creation feature are not arcane, the artificer/wizard cannot scribe them into his spellbook at all.